Help for package fDMA

Type:

Package

Title:

Dynamic Model Averaging and Dynamic Model Selection for Continuous Outcomes

Version:

2.2.8

Imports:

doParallel, forecast, foreach, gplots, graphics, grDevices, iterators, itertools, parallel, psych, png, Rcpp, stats, tseries, utils, xts, zoo

Suggests:

R.rsp

VignetteBuilder:

R.rsp

LinkingTo:

Rcpp, RcppArmadillo

Date:

2025-01-23

Author:

Krzysztof Drachal [aut, cre] (Faculty of Economic Sciences, University of Warsaw, Poland)

Maintainer:

Krzysztof Drachal <kdrachal@wne.uw.edu.pl>

Description:

Allows to estimate dynamic model averaging, dynamic model selection and median probability model. The original methods are implemented, as well as, selected further modifications of these methods. In particular the user might choose between recursive moment estimation and exponentially moving average for variance updating. Inclusion probabilities might be modified in a way using 'Google Trends'. The code is written in a way which minimises the computational burden (which is quite an obstacle for dynamic model averaging if many variables are used). For example, this package allows for parallel computations and Occam's window approach. The package is designed in a way that is hoped to be especially useful in economics and finance. Main reference: Raftery, A.E., Karny, M., Ettler, P. (2010) <doi:10.1198/TECH.2009.08104>.

License:

GPL-3

LazyData:

TRUE

URL:

https://CRAN.R-project.org/package=fDMA

Note:

Research funded by the Polish National Science Centre grant under the contract number DEC-2015/19/N/HS4/00205.

NeedsCompilation:

yes

Packaged:

2025-01-23 22:40:28 UTC; Krzysiek

Repository:

CRAN

Date/Publication:

2025-01-24 10:00:07 UTC

Computes a Few Alternative Forecasts.

Description

It is necessary to compare a given forecast method with some alternative ones. This function computes selected forecast quality measures for a few selected forecast methods (which might be treated as alternative ones to Dynamic Model Averaging, Dynamic Model Selection, etc.).

Naive forecast (naive) is computed in a way that all forecasts are set to be the value of the last observation.

For rolling OLS forecast (roll. OLS) for the first periods (until the size of a window is obtained) are estimated through recursive OLS (rec. OLS).

Autoregressive models (AR(1) and AR(2)) are computed by ordinary least squares method.

Time-varying parameters models (TVP, TVP-AR(1) and TVP-AR(2)) are computed as tvp with V=1 and lambda=0.99.

Auto ARIMA (auto ARIMA) is computed as auto.arima.

ME (Mean Error), RMSE (Root Mean Squared Error), MAE (Mean Absolute Error), MPE (Mean Percentage Errror) and MAPE (Mean Absolute Percentage Error) are computed as accuracy. HR (Hit Ratio) is computed as hit.ratio.

Usage

altf(y,x,window=NULL,initial.period=NULL,d=NULL,f=NULL,fmod=NULL,c=NULL)

Arguments

y

numeric or a column matrix of a dependent variable

x

matrix of independent variables, different columns correspond to different independent variables

window

optional, numeric, a size of a rolling regression window (a number of observations), if not specified 10% of all observations are taken

initial.period

optional, numeric, a number of observation since which forecast quality measures are computed, if not specified the whole sample is used, i.e., initial.period=1, this argument also divides the sample into in-sample and out-of-sample for non-recursive methods (OLS, AR(1), AR(2), auto ARIMA)

d

optional, logical, a parameter used for HR (Hit Ratio) calculation, should be d=FALSE for level time-series and d=TRUE if time-series represent changes, if not specified d=FALSE

f

optional, logical vector, indicating which of alternative forecasts – naive, OLS, rec. OLS, roll. OLS, TVP, AR(1), AR(2), auto ARIMA, TVP-AR(1) and TVP-AR(2) – should be computed, if not specified f=c(rep(TRUE,10)), i.e., all alternative forecasts are computed

fmod

optional, class dma object, a model to be compared with alternative forecast

c

optional, logical, a parameter indicating whether constant is included in models, if not specified c=TRUE is used, i.e., constant is included

Value

class altf object, list of

$summary

matrix of forecast quality measures ordered by columns, forecast methods are ordered by rows

$y.hat

list of predicted values from all forecasting methods which were applied

$y

y, forecasted time-series

$coeff.

list of coefficients from all forecasting methods which were applied (for naive forecast they are not computed)

$p.val.

list of p-values for t-test of statistical significance for coefficients from all forecasting methods which were applied (for naive and TVP models they are not computed, and for auto ARIMA z-test is used)

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

a1 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,initial.period=60)

# models where constant term is not included in modelled equations (if applicable)
a2 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,c=FALSE,initial.period=60)

# compute just selected models
fcomp <- c(TRUE,TRUE,TRUE,FALSE,FALSE,FALSE,TRUE,TRUE,TRUE,FALSE)
a3 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,f=fcomp,initial.period=60)

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10)
a4 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,f=fcomp,fmod=m1,initial.period=60)

Computes a Few Alternative Forecasts Based on Model Averaging.

Description

Usage

altf2(y,x,mods.incl=NULL,gprob=NULL,omega=NULL,av=NULL,window=NULL,
initial.period=NULL,d=NULL,f=NULL,fmod=NULL,parallel=NULL)

Arguments

y

numeric or a column matrix of a dependent variable

x

matrix of independent variables, different columns correspond to different independent variables

mods.incl

optional, matrix indicating which models will be used in averaging, if not specified all possible models will be used, see fDMA

gprob

optional, matrix of Google probabilities as in Koop and Onorante (2014), columns should correspond to columns of x, see fDMA

omega

optional, numeric, a parameter between 0 and 1 used in probabilities estimations, used if gprob is specified, see fDMA

av

optional, a method for model averaging, av="ord" corresponds to equal weights for each model, av="aic" corresponds to information theoretic model averaging based on Akaike Information Criterion, av="aicc" corresponds to information theoretic model averaging based on Akaike Information Criterion with a correction for finite sample sizes, av="bic" corresponds to information theoretic model averaging based on Bayesian Information Criterion, av="mse" corresponds to setting weights proportional to the inverse of the models Mean Squared Error, if not specified av="ord" is used

window

optional, numeric, a size of a rolling regression window (a number of observations), if not specified 10% of all observations are taken

initial.period

d

optional, logical, a parameter used for HR (Hit Ratio) calculation, should be d=FALSE for level time-series and d=TRUE if time-series represent changes, if not specified d=FALSE

f

optional, logical vector, indicating which of alternative forecast – av. OLS, av. rec. OLS, av. roll. OLS and av. TVP – should be averaged, if not specified f=c(rep(TRUE,4), i.e., all alternative forecast are computed

fmod

optional, class dma object, a model to be compared with alternative forecast

parallel

optional, logical, indicate whether parallel computations should be used, by default parallel=FALSE

Details

For each av method, in the initial period equal weights for each model are taken, and then successively updated based on the chosen criterion. For OLS models weights are not updated. The same weight for each model (estimated from the in-sample period) is taken for each period.

If gprob is used, then for OLS mean values from the in-sample period are taken, for rec. OLS – mean values from periods up to the current one, for roll. OLS – mean values from the last window periods, and for TVP – values from the current period.

Value

class altf2 object, list of

$summary

matrix of forecast quality measures ordered by columns, forecast methods are ordered by rows

$y.hat

list of predicted values from all forecasting methods which were applied

$y

y, forecasted time-series

$coeff.

list of coefficients from all forecasting methods which were applied

$weights

list of weights of models used in averaging for all forecasting methods which were applied

$p.val.

list of p-values (averaged with respect to suitable weights) for t-test of statistical significance for coefficients from all forecasting methods which were applied (for TVP they are not computed)

$rel.var.imp.

list of relative variable importance from all forecasting methods which were applied

$exp.var.

list of expected number of variables (incl. constant) from all forecasting methods which were applied

References

Burnham, K. P., Anderson, D. R., 2004. Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods & Research 33, 261–304.

Burnham, K. P., Anderson, D. R., 2002. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Springer.

Gelman, A., Hwang, J., Vehtari, A., 2014. Understanding predictive information criteria for Bayesian models. Statistics and Computing 24, 997–1016.

Kapetanios, G., Labhard, V., Price, S., 2008. Forecasting using Bayesian and information-theoretic model averaging. Journal of Business & Economic Statistics 26, 33–41.

Koop, G., Onorante, L., 2014. Macroeconomic nowcasting using Google probabilities. https://goo.gl/ATsBN9

Timmermann, A., 2006. Forecast combinations. In: Elliott, G., et al. (eds.), Handbook of Economic Forecasting, Elsevier.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

a1 <- altf2(y=ld.wti,x=ld.drivers,d=TRUE,initial.period=60)

# compute just selected models
fcomp <- c(TRUE,TRUE,TRUE,FALSE)
a2 <- altf2(y=ld.wti,x=ld.drivers,d=TRUE,f=fcomp,initial.period=60)
a3 <- altf2(y=ld.wti,x=ld.drivers,d=TRUE,f=fcomp,av="aic",initial.period=60)

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10)
a4 <- altf2(y=ld.wti,x=ld.drivers,d=TRUE,f=fcomp,fmod=m1,initial.period=60)

# models just with one independent variable and a constant will be averaged
mds <- diag(1,ncol(ld.drivers),ncol(ld.drivers))
mds <- cbind(rep(1,ncol(ld.drivers)),mds)
a5 <- altf2(y=ld.wti,x=ld.drivers,d=TRUE,mods.incl=mds,initial.period=60)

# Google trends are available since 2004
gp <- trends/100
s1 <- ld.wti['2004-01-01/']
s2 <- ld.drivers['2004-01-01/']
a6 <- altf2(y=s1,x=s2,d=TRUE,gprob=gp,omega=0.5,initial.period=60)

Computes a Rolling Regression Averaged over Different Window Sizes.

Description

It is necessary to compare a given forecast method with some alternative ones. This function computes selected forecast quality measures for a rolling regression averaged over different window sizes (which might be treated as alternative forecasting method to Dynamic Model Averaging, Dynamic Model Selection, etc.).

Usage

altf3(y,x=NULL,windows,av=NULL,initial.period=NULL,d=NULL,fmod=NULL,parallel=NULL,c=NULL)

Arguments

y

numeric or a column matrix of a dependent variable

x

matrix of independent variables, different columns correspond to different independent variables, if not specified only constant term will be included

windows

numeric vector, sizes of a rolling regression windows (numbers of observations)

av

initial.period

optional, numeric, a number of observation since which forecast quality measures are computed, if not specified the whole sample is used, i.e., initial.period=1

d

optional, logical, a parameter used for HR (Hit Ratio) calculation, should be d=FALSE for level time-series and d=TRUE if time-series represent changes, if not specified d=FALSE

fmod

optional, class dma object, a model to be compared with alternative forecast

parallel

optional, logical, indicate whether parallel computations should be used, by default parallel=FALSE

c

optional, see roll.reg

Details

For each av method, in the initial period equal weights for each model are taken, and then successively updated based on the chosen criterion.

Value

class altf3 object, list of

$summary

matrix of forecast quality measures ordered by columns

$y.hat

list of predicted values from a rolling regression averaged over selected window sizes

$y

y, forecasted time-series

$coeff.

list of coefficients from a rolling regression averaged over selected window sizes

$weights

list of weights of models used in averaging

$p.val.

list of p-values (averaged over selected window sizes) for t-test of statistical significance for coefficients from a rolling regression

$exp.win.

list of expected window size

References

Pesaran, M. H., Pick, A., 2011. Forecast combination across estimation windows. Journal of Business & Economic Statistics 29, 307–318.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

a1 <- altf3(y=ld.wti,x=ld.drivers,d=TRUE,windows=c(36,100,150))

a2 <- altf3(y=ld.wti,x=ld.drivers,d=TRUE,av="aic",windows=c(36,100,150))

a3 <- altf3(y=ld.wti,x=ld.drivers,d=TRUE,av=-2,windows=c(36,100,150))

# models without a constant term 
a4 <- altf3(y=ld.wti,x=ld.drivers,d=TRUE,av=-2,windows=c(36,100,150),c=FALSE)

# models only with a constant term
a5 <- altf3(y=ld.wti,d=TRUE,av=-2,windows=c(36,100,150))

Computes a Time-Varying Parameters Rolling Regression Averaged over Different Window Sizes.

Description

It is necessary to compare a given forecast method with some alternative ones. This function computes selected forecast quality measures for a time-varying parameters rolling regression averaged over different window sizes (which might be treated as alternative forecasting method to Dynamic Model Averaging, Dynamic Model Selection, etc.). The averaging is performed as in Raftery et al. (2010). The only difference is that the state space of the models are constructed not by chosing different combinations of independent variables, but for a fixed set of independent variables various rolling windows sizes are chosen and models constructed in such a way constitute the state space.

Usage

altf4(y,x,windows,V=NULL,alpha=NULL,lambda=NULL,initial.period=NULL,
d=NULL,fmod=NULL,parallel=NULL,c=NULL,small.c=NULL)

Arguments

y

numeric or a column matrix of a dependent variable

x

matrix of independent variables, different columns correspond to different independent variables

windows

numeric vector, sizes of a rolling regression windows (numbers of observations)

V

optional, numeric, initial variance in the state space equation for the recursive moment estimator updating method, as in Raftery et al. (2010), if not specified V=1 is taken, see tvp

lambda

optional, numeric, a forgetting factor between 0 and 1 used in variance approximations, if not specified lambda=0.99 is taken, see tvp

alpha

optional, numeric, a forgetting factor \alpha between 0 and 1 used in probabilities estimations, if not specified alpha=0.99 is taken, see fDMA

initial.period

optional, numeric, a number of observation since which forecast quality measures are computed, if not specified the whole sample is used, i.e., initial.period=1

d

optional, logical, a parameter used for HR (Hit Ratio) calculation, should be d=FALSE for level time-series and d=TRUE if time-series represent changes, if not specified d=FALSE

fmod

optional, class dma object, a model to be compared with alternative forecast

parallel

optional, logical, indicate whether parallel computations should be used, by default parallel=FALSE

c

optional, see tvp

small.c

optional, see fDMA

Value

class altf4 object, list of

$summary

matrix of forecast quality measures ordered by columns

$y.hat

list of predicted values from a time-varying parameters rolling regression averaged over selected window sizes

$y

y, forecasted time-series

$coeff.

list of coefficients from a time-varying parameters rolling regression averaged over selected window sizes

$weights

list of weights of models used in averaging

$exp.win.

list of expected window size

References

Pesaran, M. H., Pick, A., 2011. Forecast combination across estimation windows. Journal of Business & Economic Statistics 29, 307–318.

Raftery, A. E., Gneiting, T., Balabdaoui, F., Polakowski, M., 2005. Using Bayesian Model Averaging to calibrate forecast ensembles. Monthly Weather Review 133, 1155–1174.

Raftery, A. E., Karny, M., Ettler, P., 2010. Online prediction under model uncertainty via Dynamic Model Averaging: Application to a cold rolling mill. Technometrics 52, 52–66.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

a1 <- altf4(y=ld.wti,x=ld.drivers,d=TRUE,windows=c(36,100,150))

win <- c(36,100,150)
a2 <- altf4(y=ld.wti,x=ld.drivers,d=TRUE,windows=win,alpha=0.9,lambda=0.95)

# models without a constant term
a3 <- altf4(y=ld.wti,x=ld.drivers,d=TRUE,windows=win,alpha=0.9,lambda=0.95,c=FALSE)

# models only with a constant term
empty <- matrix(,nrow=nrow(ld.drivers),ncol=0)
a4 <- altf4(y=ld.wti,x=empty,d=TRUE,windows=win,alpha=0.9,lambda=0.95)

Computes Engle's ARCH Test.

Description

This function computes Engle's ARCH test. The null hypothesis of this Lagrange Multiplier test is that a series of residuals exhibits no ARCH effects. The alternative hypothesis is that ARCH(lag) effects are present. The lag is specified by the User.

Usage

archtest(ts,lag=NULL)

Arguments

ts

vector, the tested time-series

lag

numeric, suspected order of ARCH process, if not specified lag=1 is taken

Value

class htest object, list of

statistic

test statistic

parameter

lag used in the test

alternative

alternative hypothesis of the test

p.value

p-value

method

name of the test

data.name

name of the tested time-series

References

Engle, R. F., 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.

Examples

wti <- crudeoil[-1,1]
ld.wti <- (diff(log(wti)))[-1,]
arch <- archtest(ts=as.vector(ld.wti),lag=10)

Extracts Averaged Coefficients from `dma` Model.

Description

The function extracts the expected values of regression coefficients from the fDMA model.

Usage

## S3 method for class 'dma'
coef(object, ...)

Arguments

object

an object of dma class

...

not used

Value

matrix of expected values of regression coefficients

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dma")
c <- coef(object=m1)

Crude Oil Data.

Description

Selected data from oil market.

Usage

data(crudeoil)

Format

crudeoil is xts object such that

crudeoil$p_oil – average spot price of crude oil (Brent, Dubai and WTI) in USD per barrel
crudeoil$prod – U.S. field production of crude oil in thousand barrels
crudeoil$cons – U.S. product supplied of crude oil and petroleum products in thousand barrels
crudeoil$econ_act – Index of Global Real Economic Activity
crudeoil$r – U.S. 3-month treasury bill secondary market rate in %
crudeoil$stocks – U.S. share prices index, 2015=100
crudeoil$risk – Geopolitical risk (GPR) index
crudeoil$ex_rate – U.S. real effective exchange rate index (broad basket), 2020=100

Details

The data are in monthly frequency. They cover the period between Jan, 1998 and Oct, 2024.

Source

The data are provided by Bank for International Settlements, Board of Governors of the Federal Reserve System, Caldara and Iacoviello (2022), Federal Reserve Bank of Dallas, OECD, U.S. Energy Information Administration and World Bank.

https://www.bis.org

https://www.dallasfed.org

https://www.eia.gov

https://www.federalreserve.gov

https://www.matteoiacoviello.com/gpr.htm

https://www.oecd.org/en.html

https://www.worldbank.org/ext/en/home

References

Bank for International Settlements, 2025. Effective exchange rates, BIS WS_EER 1.0 (data set). https://data.bis.org/topics/EER/BIS%2CWS_EER%2C1.0/M.R.B.US

Board of Governors of the Federal Reserve System, 2025. Selected interest rates. https://www.federalreserve.gov/releases/h15/

Caldara, D., Iacoviello, M., 2022. Measuring geopolitical risk. American Economic Review 112, 1194–1225.

Federal Reserve Bank of Dallas, 2025. Index of global real economic activity. https://www.dallasfed.org/research/igrea

Kilian, L., 2009. Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market. American Economic Review 99, 1053–1069.

OECD, 2025. Share prices. https://www.oecd.org/en/data/indicators/share-prices.html

U.S. Energy Information Administration, 2025. Petroleum /& other liquids. https://www.eia.gov/petroleum/data.php

World Bank, 2025. Commodity markets. https://www.worldbank.org/en/research/commodity-markets

Examples

data(crudeoil)
wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dma")

Computes Basic Descriptive Statistics.

Description

This function computes descriptive statistics which are most useful for Dynamic Model Averaging.

It is a wrapper of describe.

If the argument is not a matrix, the function tries to convert the object into a matrix. For example, it works smoothly for xts objects.

Usage

descstat(data)

Arguments

data

matrix, observations are put in rows, and variables are grouped by columns

Details

See describe.

Value

matrix

Examples

descstat(crudeoil)

Computes Diebold-Mariano Test.

Description

This is a wrapper for dm.test from forecast package. This function computes the original Diebold-Mariano test.

Usage

dmtest(y,f)

Arguments

y

vector of the forecasted time-series

f

matrix of the predicted values from various methods, forecasts are ordered in rows, the first row should correspond to the method that is compared with alternative ones (corresponding to subsequent rows)

Details

The null hypothesis is that the two methods have the same forecast accuracy. This function assumes that one-step ahead forecasts are compared and the second power is used in the loss function (see dm.test). "The Diebold-Mariano (DM) test was intended for comparing forecasts; it has been, and remains, useful in that regard. The DM test was not intended for comparing models." (Diebold, 2015)

Value

matrix, first column contains tests statistics, next p-values are given for the alternative hypothesis that alternative forecasts have different accuracy than the compared forecast, alternative forecasts are less accurate and alternative forecasts have greater accuracy, tests outcomes for different forecasts are ordered by rows

References

Diebold, F. X., 2015. Comparing predictive accuracy, Twenty years later: A peersonal perspective on the use and abuse of Diebold-Mariano tests. Journal of Business & Economic Statistics 33, doi:10.1080/07350015.2014.983236.

Diebold, F. X., Mariano, R. S., 1995. Comparing predictive accuracy. Journal of Business & Economic Statistics 13, 253–263.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
m <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,initial.period=241)
m <- m$y.hat
a <- altf2(y=ld.wti,x=ld.drivers,d=TRUE,initial.period=241)
a <- a$y.hat
a <- matrix(unlist(a),nrow=length(a),byrow=TRUE)
fc <- rbind(m,a)
dm <- dmtest(y=as.vector(ld.wti)[-(1:240)],f=fc[,-(1:240)])

Computes Dynamic Model Averaging.

Description

The function estimates Dynamic Model Averaging (and some of its variations). The method is described in Raftery et al. (2010).

Usage

fDMA(y,x,alpha,lambda,initvar,W=NULL,initial.period=NULL,V.meth=NULL,kappa=NULL,
gprob=NULL,omega=NULL,model=NULL,parallel=NULL,m.prior=NULL,mods.incl=NULL,
DOW=NULL,DOW.nmods=NULL,DOW.type=NULL,DOW.limit.nmods=NULL,progress.info=NULL,
forced.models=NULL,forbidden.models=NULL,forced.variables=NULL,bm=NULL,
small.c=NULL,fcores=NULL,mods.check=NULL,red.size=NULL,av=NULL)

Arguments

y

numeric or a column matrix of a dependent variable, if y is xts object, then plots will have time index on the x axis

x

matrix of independent variables, different columns correspond to different variables

alpha

numeric, a forgetting factor \alpha between 0 and 1 used in probabilities estimations

lambda

numeric, a forgetting factor \lambda between 0 and 1 used in variance approximations

initvar

numeric, initial variance in the state space equation, i.e., the number by which the unit matrix is multiplied

W

optional, a method for setting the initial values of variance for the models equations, W="reg" corresponds to the method based on the linear regression as in the paper by Raftery et al. (2010), alternatively an arbitrary positive number (numeric) can be specified, by default the method of Raftery et al. (2010) is used

initial.period

optional, numeric, a number of observation since which MSE (Mean Squared Error) and MAE (Mean Absolute Error) are computed, by default the whole sample is used, i.e., initial.period=1

V.meth

optional, a method for the state space equation variance updating, V.meth="rec" corresponds to the recursive moment estimator, as in the paper by Raftery et al. (2010), V.meth = "ewma" corresponds to the exponentially weighted moving average as in, for example, Koop and Korobilis (2012), by default V.meth = "rec" is used

kappa

optional, numeric, a parameter in the exponentially weighted moving average, between 0 and 1, used if V.meth = "ewma"

gprob

optional, matrix of Google probabilities as in Koop and Onorante (2014), columns should correspond to columns of x

omega

optional, numeric, a parameter between 0 and 1 used in probabilities estimations, used if gprob is specified

model

optional, model="dma" for Dynamic Model Averaging, model="dms" for Dynamic Model Selection, or model="med" for Median Probability Model as in Barbieri and Berger (2004), by default model="dma" is used

parallel

optional, logical, indicate whether parallel computations should be used, by default parallel=FALSE

m.prior

optional, numeric, a parameter for general model prior (Mitchell and Beauchamp, 1988), by default m.prior=0.5, which corresponds to the uniform distribution, i.e., non-informative priors, see also Eicher et al. (2011)

mods.incl

optional, matrix indicating which models should be used for estimation, the first column indicates inclusion of a constant, by default all possible models with a constant are used, inclusion of a variable is indicated by 1, omitting by 0

DOW

optional, numeric, a threshold for Dynamic Occam's Window (Onorante and Raftery, 2016), should be a number between 0 and 1, if DOW=0, then no Dynamic Occam's Window is applied, by default DOW=0, Dynamic Occam's Window can be applied only to Dynamic Model Averaging, i.e., when model="dma"

DOW.nmods

optional, numeric, initial number of models for Dynamic Occam's Window, should be less than the number of all possible models and larger than or equal to 2, they are randomly chosen, if DOW.nmods=0, then initially models with exactly one variable are taken, by default DOW.nmods=0

DOW.type

optional, DOW.type="r" corresponds to DMA-R from Onorante and Raftery (2016), DOW.type="e" to DMA-E, by default DOW.type="r"

DOW.limit.nmods

optional, numeric, maximum number of models selected by Dynamic Occam's Window, an additional limitation to the threshold given by DOW, by default no limit is set

progress.info

optional, logical, applicable only if Dynamic Occam's Window is used, otherwise ignored, if progress.info=TRUE number of the current recursive DMA computation round and number of models selected for this round are printed, by default progress.info=FALSE

forced.models

optional, matrix, applicable only if Dynamic Occam's Window is used, otherwise ignored, indicates models that have to be always included in the set of expanded models, similar as mods.incl, by default forced.models=NULL

forbidden.models

optional, matrix, applicable only if Dynamic Occam's Window is used, otherwise ignored, indicates models that cannot be used in the set of expanded models, similar as mods.incl, by default forbidden.models=NULL

forced.variables

optional, vector, applicable only if Dynamic Occam's Window is used, otherwise ignored, indicates variables that have to be always included in models constituting the set of expanded models, similar as mods.incl, first slot indicates inclusion of constant, by default forced.variables=NULL

bm

optional, logical, indicate whether benchmark forecast should be computed, these benchmarks are naive forecast (all forecasts are set to be the value of the last observation) and Auto Arima auto.arima, by default bm=FALSE

small.c

optional, numeric, small constant added to posterior model proabilities as in Raftery et al. (2010) to prevent potential reduction them to 0 due to the computational issues, if not specified the value computed as in Raftery et al. (2010) is taken

fcores

optional, numeric, used only if parallel=TRUE, otherwise ignored, indicates the number of cores that should not be used, by default fcores=1

mods.check

optional, logical, indicates if mods.incl should be checked for duplicated entries, etc., by default mods.check=FALSE

red.size

optional, logical, indicates if outcomes should be reduced to save memory, by default red.size=FALSE

av

optional, av="dma" corresponds to the original DMA averaging scheme, av="mse" corresponds to averaging based on Mean Squared Error, av="hr1" corresponds to averaging based on Hit Ratio, assuming time-series are in levels, av="hr2" corresponds to averaging based on Hit Ratio, assuming time-series represent changes, by default av="dma"

Details

It is possible to use numeric vector for lambda. Its values are automatically ordered in descending order and if numbers are not unique they are reduced to become unique. If more than one value is given for lambda, then model state space, i.e., mods.incl, is expanded by considering all these models with given values of lambda. The outcomes are then ordered by columns in a way that first outcomes from models with first value of lambda are presented, then from models with second value of lambda, etc. (Raftery et al., 2010).

If nrow(gprob)<length(y), then the method by Koop and Onorante (2014) is used for the last nrow(gprob) observations. For the preceding ones the original method by Raftery et al. (2010) is used. In such case a warning is generated.

Value

class dma object, list of

$y.hat

forecasted values

$post.incl

posterior inclusion probabilities for independent variables

$MSE

Mean Squared Error of forecast

$MAE

Mean Absolute Error of forecast

$models

models included in estimations, or models used in the last step of Dynamic Occam's Window method (if this method has been selected)

$post.mod

posterior probabilities of all used models, or NA if Dynamic Occam's Window method has been selected

$exp.var

expected number of variables (incl. constant)

$exp.coef.

expected values of regression coefficients

$parameters

parameters of the estimated model

$yhat.all.mods

predictions from every sub-model used in estimations

$y

y, dependent variable

$benchmarks

Root Mean Squared Error and Mean Absolute Error of naive and auto ARIMA forecast

$DOW.init.mods

models initially selected to Dynamic Occam's Window, if this method has been selected

$DOW.n.mods.t

number of models used in Dynamic Model Averaging at time t, if Dynamic Occam's Window method has been selected

$p.dens.

predicitive densities from the last period of all sub-models used in estimations

$exp.lambda

expected values of lambda parameter

Source

Raftery, A. E., Karny, M., Ettler, P., 2010. Online prediction under model uncertainty via Dynamic Model Averaging: Application to a cold rolling mill. Technometrics 52, 52–66.

References

Barbieri, M. M., Berger, J. O., 2004. Optimal predictive model selection. The Annals of Statistics 32, 870–897.

Eicher, T. S., Papageorgiou, C., Raftery, A. E., 2011. Default priors and predictive performance in Bayesian Model Averaging, with application to growth determinants. Journal of Applied Econometrics 26, 30–55.

Koop, G., Korobilis, D., 2012. Forecasting inflation using Dynamic Model Averaging. International Economic Review 53, 867–886.

Koop, G., Korobilis, D., 2018. Variational Bayes inference in high-dimensional time-varying parameter models. https://arxiv.org/pdf/1809.03031

Koop, G., Onorante, L., 2014. Macroeconomic nowcasting using Google probabilities. https://goo.gl/ATsBN9

Mitchell, T. J., Beauchamp, J. J., 1988. Bayesian variable selection in linear regression (with discussion). Journal of the American Statistical Association 83, 1023–1036.

Onorante, L., Raftery, A. E., 2016. Dynamic model averaging in large model spaces using dynamic Occam's window. European Economic Review 81, 2–14.

Yin, X., Peng, J., Tang, T., 2018. Improving the forecasting accuracy of crude oil prices. Sustainability 10, 454. doi:10.3390/su10020454

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10)
m2 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,model="dms")
m3 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,V.meth="ewma",kappa=0.9)
m4 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,DOW=0.7)


# Google trends are available since 2004

gp <- trends/100
s <- ld.drivers['2004-01-01/']
m5 <- fDMA(y=ld.wti['2004-01-01/'],x=s,alpha=0.99,lambda=0.90,initvar=10,gprob=gp,omega=0.5)


# models just with one independent variable and a constant will be averaged
mds <- diag(1,ncol(ld.drivers),ncol(ld.drivers))
mds <- cbind(rep(1,ncol(ld.drivers)),mds)

m6 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,mods.incl=mds)


# models just with one independent variable (without a constant) will be averaged
mds.nc <- diag(1,ncol(ld.drivers),ncol(ld.drivers))
mds.nc <- cbind(rep(0,ncol(ld.drivers)),mds.nc)

m7 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,mods.incl=mds.nc)

# model with multiple lambda

m8 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=c(0.99,0.95,0.90),initvar=10)

Extracts Fitted Values from `dma` Model.

Description

The function extracts predictions made by the fDMA model.

Usage

## S3 method for class 'dma'
fitted(object, ...)

Arguments

object

an object of dma class

...

not used

Value

vector of forecasted values

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dma")
f <- fitted(object=m1)

Normalizes a Numeric Matrix by Rows.

Description

For example, Google Trends data are given as numbers between 0 and 100. If the Users divide them by 100, they can be interpreted in a certain sense as probabilities.

However, if there are such probabilities for several variables, sometimes it might be desirable to have the sum of these probabilities for all variables to sum up to 1. This function does not divide the values of an argument by 100, but rescales every row to sum up to 1. In other words, values in each row of an argument are divided by the sum of all values in this row.

Usage

gNormalize(data)

Arguments

data

matrix, observations are put in rows, and variables are grouped by columns

Value

matrix

References

Koop, G., Onorante, L., 2014. Macroeconomic nowcasting using Google probabilities. https://goo.gl/ATsBN9

Examples

gt <- gNormalize(trends)

gNormalize(rbind(c(0,1,2),c(1,2,3)))

Computes `fDMA` Function for Multiple Values of `alpha` and `lambda`.

Description

Sometimes it is necessary to consider various values of parameters alpha and lambda in Dynamic Model Averaging (or Dynamic Model Selection, etc.). This function computes fDMA function for all combinations of alpha and lambda for given grids.

This function is a wrapper of fDMA.

Usage

grid.DMA(y,x,grid.alpha,grid.lambda,initvar,W=NULL,initial.period=NULL,V.meth=NULL,
kappa=NULL,gprob=NULL,omega=NULL,model=NULL,parallel.grid=NULL,m.prior=NULL,
mods.incl=NULL,DOW=NULL,DOW.nmods=NULL,DOW.type=NULL,DOW.limit.nmods=NULL,
forced.models=NULL,forbidden.models=NULL,forced.variables=NULL,bm=NULL,
small.c=NULL,av=NULL)

Arguments

y

see fDMA

x

see fDMA

grid.alpha

a numeric vector of different values of alpha

grid.lambda

a numeric vector of different values of lambda or a list of numeric vectors for multiple lambda in one model (see fDMA)

initvar

see fDMA

W

see fDMA

initial.period

see fDMA

V.meth

see fDMA

kappa

see fDMA

gprob

see fDMA

omega

see fDMA

model

see fDMA

parallel.grid

optional, logical, indicate whether parallel computations should be used, by default parallel.grid=FALSE

m.prior

see fDMA

mods.incl

see fDMA

DOW

see fDMA

DOW.nmods

see fDMA

DOW.type

see fDMA

DOW.limit.nmods

see fDMA

forced.models

see fDMA

forbidden.models

see fDMA

forced.variables

see fDMA

bm

see fDMA

small.c

see fDMA

av

see fDMA

Value

an object of class grid.dma, list of

$models

list of list of models

$RMSE

matrix with Root Mean Squared Error (RMSE) for all estimated models

$MAE

matrix with Mean Absolute Error (MAE) for all estimated models

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

gra <- c(0.99,0.98,0.97)
grl <- c(0.99,0.95)
g1 <- grid.DMA(y=ld.wti,x=ld.drivers,grid.alpha=gra,grid.lambda=grl,initvar=10)


# extract model with alpha=0.97 and lambda=0.95
model <- g$models[[3]][[2]]

# models with various multiple lambdas

gra <- c(0.99,0.98,0.97)
grl <- list(c(0.99,0.95,0.90),c(0.99,0.98,0.97,0.96,0.95))
g2 <- grid.DMA(y=ld.wti,x=ld.drivers,grid.alpha=gra,grid.lambda=grl,initvar=10)

Computes `roll.reg` Function for Multiple Values of `window`.

Description

Sometimes it is necessary to consider various values of parameter window in Rolling Regression. This function computes roll.reg function for all values of window for a given grid.

This function is a wrapper of roll.reg.

Usage

grid.roll.reg(y,x=NULL,grid.window,parallel.grid=NULL,c=NULL)

Arguments

y

see roll.reg

x

see roll.reg

grid.window

a numeric vector of different values of window, see roll.reg

parallel.grid

optional, logical, indicate whether parallel computations should be used, by default parallel=FALSE

c

optional, see roll.reg

Value

an object of class grid.roll.reg, list of

$models

list of reg objects

$fq

matrix with Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) for all estimated models

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

grw <- c(50,100,150)
g <- grid.roll.reg(y=ld.wti,x=ld.drivers,grid.window=grw)

# extract model with window=100
model <- g$models[[2]]

Computes `tvp` Function for Multiple Values of `lambda`.

Description

Sometimes it is necessary to consider various values of parameter lambda in Time-Varying Parameters Regression. This function computes tvp function for all values of lambda for a given grid.

This function is a wrapper of tvp.

Usage

grid.tvp(y,x,V,grid.lambda,W=NULL,kappa=NULL,parallel.grid=NULL,c=NULL)

Arguments

y

see tvp

x

see tvp

V

see tvp

grid.lambda

a numeric vector of different values of lambda, see tvp

W

optional, see tvp

kappa

optional, see tvp

parallel.grid

optional, logical, indicate whether parallel computations should be used, by default parallel=FALSE

c

optional, see tvp

Value

an object of class grid.tvp, list of

$models

list of tvp objects

$fq

matrix with Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) for all estimated models

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

grl <- c(0.99,0.98,0.97,0.96,0.95)
g <- grid.tvp(y=ld.wti,x=ld.drivers,V=1,grid.lambda=grl)

# extract model with lambda=0.95
model <- g$models[[5]]

Computes Hit Ratio (HR) for Forecast.

Description

Sometimes it is interesting to analyze just whether the forecast can predict the direction of a change in a modelled time-series. This function computes the proportion of correctly predicted signs (i.e., in which cases the direction of a change given by forecast agrees with the change in real data).

Usage

hit.ratio(y,y.hat,d=NULL)

Arguments

y

numeric, vector, or one row or one column matrix or xts object, representing a forecasted time-series

y.hat

numeric, vector, or one row or one column matrix or xts object, representing forecast predictions

d

optional, logical, d=FALSE for level time-series, d=TRUE if time-series already represent changes, by default d=FALSE

Value

numeric

References

Baur, D. G., Beckmann, J., Czudaj, R., 2016. A melting pot – Gold price forecasts under model and parameter uncertainty. International Review of Financial Analysis 48, 282–291.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m1 <- fDMA(y=wti,x=drivers[,5:7],alpha=0.99,lambda=0.99,initvar=10)
hit.ratio(y=wti,y.hat=m1$y.hat)

m2 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=10)
hit.ratio(y=ld.wti,y.hat=m2$y.hat,d=TRUE)

Computes Diebold-Mariano Test when Presence of ARCH Effects is Suspected.

Description

This is a wrapper for dm.test from forecast package. This function computes the modified Diebold-Mariano test. The modification is useful if the presence of ARCH effects is suspected in forecast errors. It is also useful for small samples. This is a modification of mdmtest for the presence of ARCH effects in forecast errors.

Usage

hmdmtest(y,f)

Arguments

y

vector of the forecasted time-series

f

Details

Value

References

Newbold, P., Harvey, D. J., 2002. Forecast combinations. In: Clements, M. P., Hendry, D. F. (eds.), A Companion to Economic Forecasting, Blackwell Publishing Ltd.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
m <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,initial.period=241)
m <- m$y.hat
a <- altf2(y=ld.wti,x=ld.drivers,d=TRUE,initial.period=241)
a <- a$y.hat
a <- matrix(unlist(a),nrow=length(a),byrow=TRUE)
fc <- rbind(m,a)
hmdm <- hmdmtest(y=as.vector(ld.wti)[-(1:240)],f=fc[,-(1:240)])

Computes Harvey-Leybourne-Newbold Test.

Description

This is a wrapper for dm.test from forecast package. This function computes the modified Diebold-Mariano test. The modification is useful for small samples.

Usage

mdmtest(y,f)

Arguments

y

vector of the forecasted time-series

f

Details

Value

References

Harvey, D., Leybourne, S., Newbold, P., 1997. Testing the equality of prediction mean squared errors. International Journal of Forecasting 13, 281–291.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
m <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,initial.period=241)
m <- m$y.hat
a <- altf2(y=ld.wti,x=ld.drivers,d=TRUE,initial.period=241)
a <- a$y.hat
a <- matrix(unlist(a),nrow=length(a),byrow=TRUE)
fc <- rbind(m,a)
mdm <- mdmtest(y=as.vector(ld.wti)[-(1:240)],f=fc[,-(1:240)])

Normalizes a Numeric Matrix by Columns.

Description

For a variable considered to be used in Dynamic Model Averaging (or Dynamic Model Selection, etc.), sometimes it is desirable to have all its values between 0 and 1. This function rescales the values to fit between 0 and 1.

If the argument is not a matrix, the function tries to convert the object into a matrix. For example, it works smoothly for xts objects.

Usage

normalize(data)

Arguments

data

matrix, observations are put in rows, and variables are grouped by columns

Value

matrix

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]

nwti <- normalize(wti)

nd <- normalize(drivers)

normalize(cbind(c(0,1,2),c(1,2,3),c(0,1,3)))

Creates a `matrix` of one-variable models.

Description

This function simplifies working with one-variable models in, for example, fDMA. It produces a matrix corresponding to the set of models consisting of models with a constant and just one extra variable, and a model with a constant only.

Usage

onevar(x)

Arguments

x

matrix of independent variables, see mods.incl in fDMA

Value

matrix, inclusion of a variable is indicated by 1, omitting by 0

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

mds <- diag(1,ncol(ld.drivers),ncol(ld.drivers))
mds <- cbind(rep(1,ncol(ld.drivers)),mds)
mds <- rbind(rep(0,ncol(mds)),mds)
mds[1,1] <- 1

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,mods.incl=mds)

# Equivalently: 

m2 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10,mods.incl=onevar(ld.drivers))

Plots Selected Outcomes from `altf` Object.

Description

The function plots selected outcomes from altf object.

Usage

## S3 method for class 'altf'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of altf class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

After executing the command, the User is asked to choose

1 - for plotting regression coefficients in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

2 - for plotting p-values for t-test of statistical significance for regression coefficients from applied models, in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory).

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

Coefficients are plotted only for rec. OLS, roll. OLS, TVP, TVP-AR(1) and TVP-AR(2) models. P-values – for rec. OLS and roll. OLS.

It is suggested to execute graphics.off before exectuing plot command for altf object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting altf object, sometimes a legend might cover the important parts of the plot.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf(y=wti,x=drivers)

plot(a,non.interactive=TRUE)

Plots Selected Outcomes from `altf2` Object.

Description

The function plots selected outcomes from altf2 object.

Usage

## S3 method for class 'altf2'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of altf2 class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

After executing the command, the User is asked to choose

1 - for plotting expected coefficients in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

2 - for plotting p-values (averaged over selected models) for t-test of statistical significance for regression coefficients from applied models, in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

3 - for plotting weights of all models used in averaging,

4 - for plotting relative variable importance in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

5 - for plotting expected number of variables (incl. constant) from all models used in averaging.

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

It is suggested to execute graphics.off before exectuing plot command for altf2 object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting altf2 object, sometimes a legend might cover the important parts of the plot.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf2(y=wti,x=drivers[,5:7],av="aic")

plot(a,non.interactive=TRUE)

Plots Selected Outcomes from `altf3` Object.

Description

The function plots selected outcomes from altf3 object.

Usage

## S3 method for class 'altf3'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of altf3 class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

After executing the command, the User is asked to choose

1 - for plotting expected coefficients in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

2 - for plotting p-values (averaged over selected window sizes) for t-test of statistical significance for coefficients from a rolling regression, in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

3 - for plotting weights of all models used in averaging,

4 - for plotting expected window size.

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

It is suggested to execute graphics.off before exectuing plot command for altf3 object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting altf3 object, sometimes a legend might cover the important parts of the plot.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf3(y=wti,x=drivers,windows=c(36,100,150))

plot(a,non.interactive=TRUE)

Plots Selected Outcomes from `altf4` Object.

Description

The function plots selected outcomes from altf4 object.

Usage

## S3 method for class 'altf4'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of altf4 class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

After executing the command, the User is asked to choose

1 - for plotting expected coefficients in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

2 - for plotting weights of all models used in averaging,

3 - for plotting expected window size.

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

It is suggested to execute graphics.off before exectuing plot command for altf4 object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting altf4 object, sometimes a legend might cover the important parts of the plot.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf4(y=wti,x=drivers,windows=c(36,100,150))

plot(a,non.interactive=TRUE)

Plots Selected Outcomes from `fDMA` Function.

Description

The function plots selected outcomes from fDMA.

Usage

## S3 method for class 'dma'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of dma class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

If x comes from estimation of Dynamic Model Averaging (DMA), after executing the command, the User is asked to choose

1 - for plotting actual and predicted values,

2 - for plotting residuals,

3 - for plotting the expected number of variables (including constant),

4 - for plotting posterior inclusion probabilities (including constant) on one plot,

5 - for plotting posterior inclusion probabilities (including constant) in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

6 - for plotting expected coefficients (including constant) on one plot,

7 - for plotting expected coefficients (including constant) in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

8 - for plotting the expected value of lambda,

9 - for plotting posterior model probabilities, if Dynamic Occam's Window method has not been selected, or plotting the number of models used in Dynamic Model Averaging, if Dynamic Occam's Window method has been selected.

Chosing 0 exits the plot command.

—————————————

If x comes from estimation of Dynamic Model Selection (DMS) or Median Probability Model (MED), after executing plot the User is asked to choose

1 - for plotting actual and predicted values,

2 - for plotting residuals,

3 - for plotting the expected number of variables (including constant),

4 - for producing a plot showing which variables (including constant) are included in the DMS or MED model in each time,

5 - for plotting expected coefficients (including constant) on one plot,

6 - for plotting expected coefficients (including constant) in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

7 - for plotting the expected value of lambda (only for DMS).

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

It is suggested to execute graphics.off before exectuing plot command for dma object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting dma object, sometimes a legend might cover the important parts of the plot.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dma")
m2 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dms")

# graphics.off()
plot(m1,non.interactive=TRUE)
# graphics.off()
plot(m2,non.interactive=TRUE)

Plots Selected Outcomes from `grid.DMA` Function.

Description

The function plots selected outcomes from grid.DMA.

Usage

## S3 method for class 'grid.dma'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of grid.dma class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

If x comes from estimation of Dynamic Model Averaging (DMA), after executing the command, the User is asked to choose

1 - for plotting Root Mean Squared Error (RMSE) for all estimated models,

2 - for plotting Mean Absolute Error (MAE) for all estimated models,

3 - for plotting posterior inclusion probabilities (including constant) for all estimated models, the outcomes are saved in separate png files in the temporary directory, and additionally, plots for different variables are collected into one big plot (also saved as a png file in the temporary directory),

4 - for plotting expected coefficients (including constant) for all estimated models, the outcomes are saved in separate png files in the temporary directory, and additionally, plots for different variables are collected into one big plot (also saved as a png file in the temporary directory).

Chosing 0 exits the plot command.

—————————————

If x comes from estimation of Dynamic Model Selection (DMS) or Median Probability Model (MED), after executing the command, the User is asked to choose

1 - for plotting Root Mean Squared Error (RMSE) for all estimated models,

2 - for plotting Mean Absolute Error (MAE) for all estimated models,

3 - for plotting expected coefficients (including constant) for all estimated models, the outcomes are saved in separate png files in the temporary directory, and additionally, plots for different variables are collected into one big plot (also saved as a png file in the temporary directory).

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

It is suggested to execute graphics.off before exectuing plot command for grid.dma object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting grid.dma object, sometimes a legend might cover the important parts of the plot.

If any of the models comes from using multiple lambda (see fDMA), then RMSE and MAE are not plotted.

Also, if length(grid.alpha) or length(grid.lambda) is less than 2, then RMSE and MAE are not plotted.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
gra <- c(0.99,0.98,0.97)
grl <- c(0.99,0.95)

g1 <- grid.DMA(y=ld.wti,x=ld.drivers,grid.alpha=gra,grid.lambda=grl,initvar=1)
g2 <- grid.DMA(y=ld.wti,x=ld.drivers,grid.alpha=gra,grid.lambda=grl,initvar=1,model="dms")

# graphics.off()
plot(g1,non.interactive=TRUE)
# graphics.off()
plot(g2,non.interactive=TRUE)

Plots Selected Outcomes from `grid.roll.reg` Function.

Description

The function plots selected outcomes from grid.roll.reg.

Usage

## S3 method for class 'grid.roll.reg'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of grid.roll.reg class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

After executing the command, the User is asked to choose

1 - for plotting Root Mean Squared Error (RMSE) for all estimated models,

2 - for plotting Mean Absolute Error (MAE) for all estimated models,

3 - for plotting coefficients (including constant) for all estimated models, the outcomes are saved in separate png files in the temporary directory, and additionally, plots for different variables are collected into one big plot (also saved as a png file in the temporary directory),

4 - for plotting p-values for t-test of statistical significance for regression coefficients for all estimated models, the outcomes are saved in separate png files in the temporary directory, and additionally, plots for different variables are collected into one big plot (also saved as a png file in the temporary directory),

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

It is suggested to execute graphics.off before exectuing plot command for grid.roll.reg object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting grid.roll.reg object, sometimes a legend might cover the important parts of the plot.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

grw <- c(50,100,150)
g <- grid.roll.reg(y=ld.wti,x=ld.drivers,grid.window=grw)

plot(g,non.interactive=TRUE)

Plots Selected Outcomes from `grid.tvp` Function.

Description

The function plots selected outcomes from grid.tvp.

Usage

## S3 method for class 'grid.tvp'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of grid.tvp class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

After executing the command, the User is asked to choose

1 - for plotting Root Mean Squared Error (RMSE) for all estimated models,

2 - for plotting Mean Absolute Error (MAE) for all estimated models,

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

It is suggested to execute graphics.off before exectuing plot command for grid.tvp object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting grid.tvp object, sometimes a legend might cover the important parts of the plot.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

grl <- c(0.99,0.98,0.97,0.96,0.95)
g <- grid.tvp(y=ld.wti,x=ld.drivers,V=1,grid.lambda=grl)

plot(g,non.interactive=TRUE)

Plots Selected Outcomes from `reg` Object.

Description

The function plots selected outcomes from reg object.

Usage

## S3 method for class 'reg'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of reg class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

After executing the command, the User is asked to choose

1 - for plotting actual and predicted values,

2 - for plotting residuals,

3 - for plotting regression coefficients on one plot,

4 - for plotting regression coefficients in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory),

5 - for plotting p-values for t-test of statistical significance for regression coefficients on one plot,

6 - for plotting p-values for t-test of statistical significance for regression coefficients in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory).

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

It is suggested to execute graphics.off before exectuing plot command for reg object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting reg object, sometimes a legend might cover the important parts of the plot.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

roll <- roll.reg(y=ld.wti,x=ld.drivers,window=100)

rec <- rec.reg(y=ld.wti,x=ld.drivers)

# graphics.off()
plot(roll,non.interactive=TRUE)

# graphics.off()
plot(rec,non.interactive=TRUE)

Plots Selected Outcomes from `tvp` Object.

Description

The function plots selected outcomes from tvp object.

Usage

## S3 method for class 'tvp'
plot(x,non.interactive=NULL, ...)

Arguments

x

an object of tvp class

non.interactive

optional, logical, indicate whether plots should be made in non-interactive mode, by default non.interactive=FALSE, i.e., the user specifies in the interactive menu which plots will be made

...

not used

Details

After executing the command, the User is asked to choose

1 - for plotting actual and predicted values,

2 - for plotting residuals,

3 - for plotting regression coefficients on one plot,

4 - for plotting regression coefficients in separate png files, saved in the temporary directory, and moreover, to paste them into one big plot (also saved as a png file in the temporary directory).

Chosing 0 exits the plot command.

If non.interactive=TRUE all the above plots are made.

Value

Called for making a plot.

Note

It is suggested to execute graphics.off before exectuing plot command for tvp object. However, the User should take care to save all other plots before executing this command, as they can be lost.

If graphics.off is not executed before plotting tvp object, sometimes a legend might cover the important parts of the plot.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

tvp <- tvp(y=ld.wti,x=ld.drivers,V=1,lambda=0.99)

# graphics.off()
plot(tvp,non.interactive=TRUE)

Computes Predictions from `dma` Model.

Description

The function computes predictions based on the model obtained from fDMA.

Usage

## S3 method for class 'dma'
predict(object, newdata, type, ...)

Arguments

object

an object of dma class

newdata

a matrix as x object in fDMA

type

type="backward" computes predictions of y with the already estimated coefficients, but with x given by newdata, type="forward" computes predictions of y with the coefficients estimated in the last period, for various combinations of x given in rows of newdata

...

not used

Value

vector of forecasted values

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dma")
p1 <- predict(object=m1,newdata=ld.drivers,type="backward")
p2 <- predict(object=m1,newdata=ld.drivers[1,],type="forward")
p3 <- predict(object=m1,newdata=ld.drivers[1:3,],type="forward")

Prints `altf` Object.

Description

The function prints selected outcomes obtained from altf.

Usage

## S3 method for class 'altf'
print(x, ...)

Arguments

x

an object of altf class

...

not used

Details

The function prints forecast quality measures from x. For details see accuracy.

Value

Called for printing.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf(y=wti,x=drivers)

print(a)

Prints `altf2` Object.

Description

The function prints selected outcomes obtained from altf2.

Usage

## S3 method for class 'altf2'
print(x, ...)

Arguments

x

an object of altf2 class

...

not used

Details

The function prints forecast quality measures from x. For details see accuracy.

Value

Called for printing.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf2(y=wti,x=drivers[,5:7])

print(a)

Prints `altf3` Object.

Description

The function prints selected outcomes obtained from altf3.

Usage

## S3 method for class 'altf3'
print(x, ...)

Arguments

x

an object of altf3 class

...

not used

Details

The function prints forecast quality measures from x. For details see accuracy.

Value

Called for printing.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf3(y=wti,x=drivers,windows=c(36,100,150))

print(a)

Prints `altf4` Object.

Description

The function prints selected outcomes obtained from altf4.

Usage

## S3 method for class 'altf4'
print(x, ...)

Arguments

x

an object of altf4 class

...

not used

Details

The function prints forecast quality measures from x. For details see accuracy.

Value

Called for printing.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf4(y=wti,x=drivers,windows=c(36,100,150))

print(a)

Prints `dma` Object.

Description

The function prints selected outcomes obtained from fDMA.

Usage

## S3 method for class 'dma'
print(x, ...)

Arguments

x

an object of dma class

...

not used

Details

The function prints parameters of an argument x, Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) from the estimated model. It also shows the number of observations, the number of models in averaging (selecting) procedure and the number of variables (including constant) used in the model. The number of models does not include the increase, if multiple lambda is used. The function also shows forecast quality measures for alternative forecasting methods, i.e., naive forecast (see also altf) and, if computed, for Auto ARIMA auto.arima.

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dma")
m2 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dms")


print(m1)
print(m2)

Prints `grid.dma` Object.

Description

The function prints selected outcomes obtained from grid.DMA.

Usage

## S3 method for class 'grid.dma'
print(x, ...)

Arguments

x

an object of grid.dma class

...

not used

Details

The function prints Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) for all estimated models.

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

gra <- c(0.99,0.98,0.97)
grl <- c(0.99,0.95)
g1 <- grid.DMA(y=ld.wti,x=ld.drivers,grid.alpha=gra,grid.lambda=grl,initvar=1)
g2 <- grid.DMA(y=ld.wti,x=ld.drivers,grid.alpha=gra,grid.lambda=grl,initvar=1,model="dms")


print(g1)
print(g2)

Prints `grid.roll.reg` Object.

Description

The function prints selected outcomes obtained from grid.roll.reg.

Usage

## S3 method for class 'grid.roll.reg'
print(x, ...)

Arguments

x

an object of grid.roll.reg class

...

not used

Details

The function prints Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) for all estimated models.

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

grw <- c(50,100,150)
g <- grid.roll.reg(y=ld.wti,x=ld.drivers,grid.window=grw)

print(g)

Prints `grid.tvp` Object.

Description

The function prints selected outcomes obtained from grid.tvp.

Usage

## S3 method for class 'grid.tvp'
print(x, ...)

Arguments

x

an object of grid.tvp class

...

not used

Details

The function prints Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) for all estimated models.

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

grl <- c(0.99,0.98,0.97,0.96,0.95)
g <- grid.tvp(y=ld.wti,x=ld.drivers,V=1,grid.lambda=grl)

print(g)

Prints `reg` Object.

Description

The function prints selected outcomes obtained from roll.reg and rec.reg.

Usage

## S3 method for class 'reg'
print(x, ...)

Arguments

x

an object of reg class

...

not used

Details

The function prints mean regression coefficients from the analyzed period, Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) from the estimated model. For roll.reg it also shows the size of a rolling window.

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
roll <- roll.reg(y=ld.wti,x=ld.drivers,window=100)
rec <-  rec.reg(y=ld.wti,x=ld.drivers)
print(roll)
print(rec)

Prints `tvp` Object.

Description

The function prints selected outcomes obtained from tvp.

Usage

## S3 method for class 'tvp'
print(x, ...)

Arguments

x

an object of tvp class

...

not used

Details

The function prints mean regression coefficients from the analyzed period, Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) from the estimated model.

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
tvp <- tvp(y=ld.wti,x=ld.drivers,V=1,lambda=0.99)
print(tvp)

Computes Recursive Regression.

Description

This function computes Recursive Regression.

Usage

rec.reg(y,x=NULL,c=NULL)

Arguments

y

numeric or a column matrix of a dependent variable

x

matrix of independent variables, different columns should correspond to different variables, if not specified only a constant will be used

c

optional, logical, a parameter indicating whether constant is included, if not specified c=TRUE is used, i.e., constant is included

Details

It might happen during computations that lm (which is used inside rec.reg) will produce NA or NaN. In such a case regression coefficients for a given period are taken as 0 and p-values for t-test for statistical significance of regression coefficients are taken as 1.

It is not possible to set c=FALSE if x=NULL. In such a case the function will automatically reset c=TRUE inside the code.

Value

class reg object, list of

$y.hat

fitted (forecasted) values

$AIC

Akaike Information Criterion (from the current set of observations)

$AICc

Akaike Information Criterion with a correction for finite sample sizes (from the current set of observations)

$BIC

Bayesian Information Criterion (from the current set of observations)

$MSE

Mean Squared Error (from the current set of observations)

$coeff.

regression coefficients

$p.val

p-values for t-test for statistical significance of regression coefficients

$y

y, forecasted time-series

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
rec1 <- rec.reg(y=ld.wti,x=ld.drivers)
rec2 <- rec.reg(y=ld.wti)

Reduces the Size of `fDMA` or `grid.DMA` Outcomes.

Description

This functions reduces the size of dma or grid.dma object.

Usage

reduce.size(dma.object)

Arguments

dma.object

dma or grid.dma object

Details

The information corresponding to each sub-model is erased. In particular, for the object produced by fDMA $models is reduced to one-row matrix to keep only colnames, and $postmod, $yhat.all.mods and $p.dens. are replaced by NA. It can be useful if large number of models is considered.

Value

dma or grid.dma object, with the information corresponding to each sub-model erased

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10)
m2 <- reduce.size(m1)

Extracts Residuals from `dma` Model.

Description

The function extracts residuals from the fDMA model.

Usage

## S3 method for class 'dma'
residuals(object, ...)

Arguments

object

an object of dma class

...

not used

Value

vector of residuals

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dma")
r <- residuals(object=m1)

Computes Rolling Regression.

Description

This function computes Rolling Regression. For the first window-1 observations Recursive Regression is computed. Since window-th observation the rolling is performed.

Usage

roll.reg(y,x=NULL,window,c=NULL)

Arguments

y

numeric or a column matrix of a dependent variable

x

matrix of independent variables, different columns should correspond to different variables, if not specified only a constant will be used

window

numeric, a size of a window for rolling

c

optional, logical, a parameter indicating whether constant is included, if not specified c=TRUE is used, i.e., constant is included

Details

It might happen during computations that lm (which is used inside roll.reg) will produce NA or NaN. In such a case regression coefficients for a given period are taken as 0 and p-values for t-test for statistical significance of regression coefficients are taken as 1.

It is not possible to set c=FALSE if x=NULL. In such a case the function will automatically reset c=TRUE inside the code.

Value

class reg object, list of

$y.hat

fitted (forecasted) values

$AIC

Akaike Information Criterion (from the current window size)

$AICc

Akaike Information Criterion with a correction for finite sample sizes (from the current window size)

$BIC

Bayesian Information Criterion (from the current window size)

$MSE

Mean Squared Error (from the current window size)

$coeff.

regression coefficients

$p.val

p-values for t-test for statistical significance of regression coefficients

$window

window size

$y

y, forecasted time-series

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
roll1 <- roll.reg(y=ld.wti,x=ld.drivers,window=100)
roll2 <- roll.reg(y=ld.wti,window=100)

Extracts Relative Variable Importances from `fDMA` Model.

Description

This functions extracts posterior inclusion probabilities for independent variables from dma object.

Usage

rvi(dma.object)

Arguments

dma.object

dma object

Value

matrix of posterior inclusion probabilities for independent variables

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10)
r <- rvi(m1)

Standardizes a Numeric Matrix by Columns.

Description

Sometimes it is desirable to have all variables to have mean 0 and standard deviation 1. This function rescales the values in such a way.

If the argument is not a matrix, the function tries to convert the object into a matrix. For example, it works smoothly for xts objects.

Usage

standardize(data)

Arguments

data

matrix, observations are put in rows, and variables are grouped by columns

Value

matrix

Examples

standardize(crudeoil)

Computes a Few Stationarity Tests.

Description

This is a wrapper for three functions from tseries package. Augmented Dickey-Fuller (ADF, adf.test), Phillips-Perron (PP, pp.test) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS, kpss.test) tests for stationarity are performed.

Usage

stest(data)

Arguments

data

matrix of variables, different columns correspond to different variables

Value

matrix, tests statistics and p-values are given by columns, tests outcomes for different variables are ordered by rows

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
x <- cbind(ld.wti,ld.drivers)
stest(x)

Summarizes Outcomes from `altf` Object.

Description

The function summarizes selected outcomes obtained from altf.

Usage

## S3 method for class 'altf'
summary(object, ...)

Arguments

object

an object of altf class

...

not used

Details

The function produces the outcomes as print.altf.

Additionally, it provides mean values of coefficients and how often p-values for t-test of statistical significance for each independent variable in the model are below 1%, 5% and 10%, respectively.

Value

Called for printing.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf(y=wti,x=drivers)

summary(a)

Summarizes Outcomes from `altf2` Object.

Description

The function summarizes selected outcomes obtained from altf2.

Usage

## S3 method for class 'altf2'
summary(object, ...)

Arguments

object

an object of altf2 class

...

not used

Details

The function produces the outcomes as print.altf2.

Additionally, it provides mean values of coefficients, min, max and mean relative variable importance for each independent variable in the model, frequency when relative variable importance is over 0.5 for each independent variable in the model, and how often p-values (averaged over selected models) for t-test of statistical significance for each independent variable in the model are below 1%, 5% and 10%, respectively.

Value

Called for printing.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf2(y=wti,x=drivers[,5:7],initial.period=60)

summary(a)

Summarizes Outcomes from `altf3` Object.

Description

The function summarizes selected outcomes obtained from altf3.

Usage

## S3 method for class 'altf3'
summary(object, ...)

Arguments

object

an object of altf3 class

...

not used

Details

The function produces the outcomes as print.altf3.

Additionally, it provides mean values of coefficients and how often p-values (averaged over selected window sizes) for t-test of statistical significance for each independent variable in the model are below 1%, 5% and 10%, respectively.

Value

Called for printing.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf3(y=wti,x=drivers,windows=c(36,100,150))

summary(a)

Summarizes Outcomes from `altf4` Object.

Description

The function summarizes selected outcomes obtained from altf4.

Usage

## S3 method for class 'altf4'
summary(object, ...)

Arguments

object

an object of altf4 class

...

not used

Details

The function produces the outcomes as print.altf4.

Additionally, it provides mean values of coefficients.

Value

Called for printing.

Examples


wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
a <- altf4(y=wti,x=drivers,windows=c(36,100,150))

summary(a)

Summarizes Outcomes from `dma` Object.

Description

The function summarizes outcomes obtained from fDMA.

Usage

## S3 method for class 'dma'
summary(object, ...)

Arguments

object

an object of dma class

...

not used

Details

The function produces the outcomes as print.dma.

Additionally:

If object comes from Dynamic Model Averaging (DMA), it shows how often (in comparision to the whole analyzed period) a posterior inclusion probability for a given variable exceeds 1/2. It also shows minimum, maximum and mean posterior inclusion probability for every variable throughout the analyzed period.

If object comes from Dynamic Model Selection (DMS) or Median Probability Model (MED), it shows how often (in comparision to the whole analyzed period) a given variable is present in the selected model.

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dma")
m2 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.99,initvar=1,model="dms")


summary(m1)
summary(m2)

Summarizes Outcomes from `grid.dma` Objects.

Description

The function summarizes outcomes obtained from grid.DMA.

Usage

## S3 method for class 'grid.dma'
summary(object, ...)

Arguments

object

an object of grid.dma class

...

not used

Details

The function produces the outcomes as print.grid.dma.

Additionally, it finds the indices for a model minimizing Root Mean Squared Error (RMSE) and for a model minimizing Mean Absolute Error (MAE).

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

gra <- c(0.99,0.98,0.97)
grl <- c(0.99,0.95)
g1 <- grid.DMA(y=ld.wti,x=ld.drivers,grid.alpha=gra,grid.lambda=grl,initvar=1)
g2 <- grid.DMA(y=ld.wti,x=ld.drivers,grid.alpha=gra,grid.lambda=grl,initvar=1,model="dms")


summary(g1)
summary(g2)

Summarizes Outcomes from `grid.roll.reg` Objects.

Description

The function summarizes outcomes obtained from grid.roll.reg.

Usage

## S3 method for class 'grid.roll.reg'
summary(object, ...)

Arguments

object

an object of grid.roll.reg class

...

not used

Details

The function produces the outcomes as print.grid.roll.reg.

Additionally, it finds the model minimizing Root Mean Squared Error (RMSE) and minimizing Mean Absolute Error (MAE).

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

grw <- c(50,100,150)
g <- grid.roll.reg(y=ld.wti,x=ld.drivers,grid.window=grw)

summary(g)

Summarizes Outcomes from `grid.tvp` Objects.

Description

The function summarizes outcomes obtained from grid.tvp.

Usage

## S3 method for class 'grid.tvp'
summary(object, ...)

Arguments

object

an object of grid.tvp class

...

not used

Details

The function produces the outcomes as print.grid.tvp.

Additionally, it finds the model minimizing Root Mean Squared Error (RMSE) and minimizing Mean Absolute Error (MAE).

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

grl <- c(0.99,0.98,0.97,0.96,0.95)
g <- grid.tvp(y=ld.wti,x=ld.drivers,V=1,grid.lambda=grl)

summary(g)

Summarizes Outcomes from `reg` Object.

Description

The function summarizes selected outcomes obtained from roll.reg and rec.reg.

Usage

## S3 method for class 'reg'
summary(object, ...)

Arguments

object

an object of reg class

...

not used

Details

The function produces the outcomes as print.reg.

Additionally, it provides how often p-values for t-test of statistical significance for each independent variable in the model is below 1%, 5% and 10%, respectively.

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
roll <- roll.reg(y=ld.wti,x=ld.drivers,window=100)
rec <- rec.reg(y=ld.wti,x=ld.drivers)
summary(roll)
summary(rec)

Summarizes Outcomes from `tvp` Object.

Description

The function summarizes selected outcomes obtained from tvp.

Usage

## S3 method for class 'tvp'
summary(object, ...)

Arguments

object

an object of tvp class

...

not used

Details

The function produces the outcomes as tvp.

Value

Called for printing.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
tvp <- tvp(y=ld.wti,x=ld.drivers,V=1,lambda=0.99)
summary(tvp)

Google Trends for Crude Oil Data.

Description

Google Trends for Crude Oil Data.

Usage

data(trends)

Format

trends is xts object such that

trends$prod – Google Trends for "oil production"
trends$cons – Google Trends for "oil consumption"
trends$econ_act – Google Trends for "economic activity"
trends$r – Google Trends for "interest rate"
trends$stocks – Google Trends for "stock markets"
trends$risk – Google Trends for "market stress"
trends$ex_rate – Google Trends for "exchange rate"

Details

The data are in monthly frequency. They cover the period between Jan, 2004 and Oct, 2024.

Source

The data are provided by Google.

https://trends.google.com/trends

Examples

data(trends)
gtrends <- trends/100
data(crudeoil)
wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100
ld.wti <- ld.wti['2004-01-01-/']
ld.drivers <- ld.drivers['2004-01-01-/']

xx <- ld.drivers
m <- fDMA(y=ld.wti,x=xx,alpha=0.99,lambda=0.99,initvar=1,model="dma",gprob=gtrends,omega=0.5)

Computes Time-Varying Parameters Regression.

Description

This function computes Time-Varying Parameters Regression (TVP) with the updating procedure as in Raftery et. al (2010).

Usage

tvp(y,x,V,lambda,W=NULL,kappa=NULL,c=NULL)

Arguments

y

numeric or a column matrix of a dependent variable

x

matrix of independent variables, different columns should correspond to different variables

V

numeric, initial variance in the state space equation for the recursive moment estimator updating method, as in Raftery et al. (2010)

lambda

numeric, a forgetting factor between 0 and 1 used in variance approximations

W

optional, numeric, initial value of variance for the model equations, if not specified the method based on the linear regression, as in Raftery et al. (2010) is used

kappa

optional, numeric, a parameter in the exponentially weighted moving average in variance updating (see also fDMA), between 0 and 1, if not specified the method as in Raftery et al. (2010) is used

c

optional, logical, a parameter indicating whether constant is included, if not specified c=TRUE is used, i.e., constant is included

Details

It is not possible to set c=FALSE if ncol(x)=0. In such a case the function will automatically reset c=TRUE inside the code.

Value

class tvp object, list of

$y.hat

fitted (forecasted) values

$thetas

estimated regression coefficients

$pred.dens.

predicitive densities from each period

$y

y, forecasted time-series

References

Raftery, A. E., Karny, M., Ettler, P., 2010. Online prediction under model uncertainty via Dynamic Model Averaging: Application to a cold rolling mill. Technometrics 52, 52–66.

Sanderson, C., Curtin, R., 2016. Armadillo: A template-based C++ library for linear algebra. Journal of Open Source Software 1, https://arma.sourceforge.net/armadillo_joss_2016.pdf.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- drivers[-1,]
ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,]
ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,]
ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100

t1 <- tvp(y=ld.wti,x=ld.drivers,V=1,lambda=0.99)



t2 <- tvp(y=ld.wti,x=ld.drivers,V=1,lambda=0.99,W=1)



t3 <- tvp(y=ld.wti,x=ld.drivers,V=1,lambda=0.99,W=1,kappa=0.75)


# Model with constant only
empty <- matrix(,nrow=nrow(ld.drivers),ncol=0)
t4 <- tvp(y=ld.wti,x=empty,lambda=0.99,V=1)

Computes a Few Alternative Forecasts.

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Computes a Few Alternative Forecasts Based on Model Averaging.

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Computes a Rolling Regression Averaged over Different Window Sizes.

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Computes a Time-Varying Parameters Rolling Regression Averaged over Different Window Sizes.

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Computes Engle's ARCH Test.

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Extracts Averaged Coefficients from dma Model.

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Crude Oil Data.

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Computes Basic Descriptive Statistics.

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Computes Diebold-Mariano Test.

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Computes Dynamic Model Averaging.

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Extracts Averaged Coefficients from `dma` Model.

Extracts Fitted Values from `dma` Model.

Computes `fDMA` Function for Multiple Values of `alpha` and `lambda`.

Computes `roll.reg` Function for Multiple Values of `window`.

Computes `tvp` Function for Multiple Values of `lambda`.

Creates a `matrix` of one-variable models.