Variance forecasting with 'larch' models

Generate out-of-sample variance forecasts up to n.ahead steps ahead. Optionally, quantiles of the forecasts are also returned if the argument probs is specified. The forecasts, confidence intervals and quantiles are obtained via simulation. By default, 5000 simulations is used, but this can be changed via the n.sim argument. Also by default, the simulations uses a classical bootstrap to sample from the standardised residuals. To use an alternative set of standardised innovations, for example the standard normal, use the innov argument

Usage

# S3 method for class 'larch'
predict(object, n.ahead=12, newvxreg=NULL, newindex=NULL, 
    n.sim=NULL, innov=NULL, probs=NULL, quantile.type=7, verbose = FALSE, ...)

Arguments

object: an object of class 'larch'
n.ahead: integer that determines how many steps ahead predictions should be generated (the default is 12)
newvxreg: a matrix of n.ahead rows and NCOL(vxreg) columns with the out-of-sample values of the vxreg regressors
newindex: NULL (default) or the date-index for the zoo object returned by predict.larch. If NULL, then the function uses the in-sample index to generate the out-of-sample index
n.sim: NULL (default) or an integer, the number of replications used for the generation of the forecasts. If NULL, the number of simulations is determined internally (usually 5000)
innov: NULL (default) or a vector of length n.ahead * n.sim containing the standardised errors (i.e. mean zero and unit variance) used for the forecast simulations. If NULL, then a classic bootstrap procedure is used to draw from the standardised in-sample residuals
probs: NULL (default) or a vector with the quantile-levels (values strictly between 0 and 1) of the forecast distribution. If NULL, then no quantiles are returned
quantile.type: an integer between 1 and 9 that selects which algorithm to be used in computing the quantiles, see the argument type in quantile
verbose: logical with default FALSE. If TRUE, then additional information (typically the quantiles and/or the simulated series) used in the generation of forecasts is returned. If FALSE, then only the forecasts are returned
...: additional arguments

Value

a vector of class zoo containing the out-of-sample forecasts, or a matrix of class zoo containing the out-of-sample forecasts together with additional information (e.g. the prediction-quantiles)

Details

No details for the moment.

Author

Genaro Sucarrat, https://www.sucarrat.net/

Examples

##Simulate some data:
set.seed(123)
e <- rnorm(40)

##estimate log-ARCH(1) model:
mymod <- larch(e, arch=1)

##generate out-of-sample forecasts:
predict(mymod)
#>        41        42        43        44        45        46        47        48 
#> 0.8170129 0.7904251 0.7891456 0.7900300 0.7893880 0.7912624 0.7874184 0.7931848 
#>        49        50        51        52 
#> 0.7909795 0.7920767 0.7898949 0.7908645 

##same, but return also selected quantiles:
predict(mymod, probs=c(0.10,0.90))
#>          sd2      q0.1      q0.9
#> 41 0.8170129 0.8170129 0.8170129
#> 42 0.7889723 0.7047023 0.8926209
#> 43 0.7914196 0.7082388 0.9141842
#> 44 0.7918035 0.7081293 0.9142889
#> 45 0.7918120 0.7100031 0.9176080
#> 46 0.7898864 0.7082053 0.9176523
#> 47 0.7914346 0.7092270 0.9121551
#> 48 0.7908053 0.7075605 0.9120371
#> 49 0.7906303 0.7056429 0.9140266
#> 50 0.7900909 0.7073553 0.9176142
#> 51 0.7894340 0.7066438 0.8989683
#> 52 0.7908136 0.7075815 0.9176056

##same, but using standard normals (instead of bootstrap) in the simulations:
n.sim <- 2000
n.ahead <- 12 #the default on n.ahead
predict(mymod, probs=c(0.10,0.90), n.sim=n.sim, innov=rnorm(n.ahead*n.sim))
#>          sd2      q0.1      q0.9
#> 41 0.8170129 0.8170129 0.8170129
#> 42 0.8042051 0.7110091 0.9296428
#> 43 0.8043217 0.7116390 0.9266204
#> 44 0.8035386 0.7129277 0.9195822
#> 45 0.8029674 0.7115389 0.9169221
#> 46 0.8027409 0.7117134 0.9186196
#> 47 0.8018033 0.7109971 0.9221035
#> 48 0.8058531 0.7123469 0.9229128
#> 49 0.8056665 0.7118974 0.9271428
#> 50 0.8044520 0.7134699 0.9295316
#> 51 0.8068406 0.7127420 0.9309104
#> 52 0.8057668 0.7117767 0.9252066

##make x-regressors:
x <- matrix(rnorm(40*2), 40, 2)

##estimate log-ARCH(1) model w/covariates:
mymod <- larch(e, arch=1, vxreg=x)

##predict up to 5 steps ahead, setting x's to 0 out-of-sample:
predict(mymod, n.ahead=5, newvxreg=matrix(0,5,NCOL(x)))
#>        41        42        43        44        45 
#> 0.8036733 0.7764522 0.7796526 0.7778416 0.7774535