# Should VAR(1) and VAR(1)-GARCH(1,1) give equal point forecasts out of sample?

I have a VAR(1) with heteroscedastic errors, so I used the rmgarch package for R to estimate a VAR(1)-GARCH(1,1). After that I performed an out-sample forecast for the mean equation with both models. They give me the exact same result with GARCH or without. Is that suppose to happen?

I will provide the code that I'm using:

    ## VAR(1) ##

library("vars")

Data <- betas[-c(163,164), ]

var1 <- VAR(Data, p = 1, type = "const",
season = NULL, exogen = NULL, lag.max = NULL,
ic = c("AIC", "HQ", "SC", "FPE"))

var.predict <- predict(var1, n.ahead = 2, ci = 0.95)

## VAR(1)-GARCH(1,1) ##

library(rmgarch)

uspec = ugarchspec(mean.model = list(armaOrder = c(0,0), include.mean =
FALSE),
variance.model = list(garchOrder = c(1,1), model = "sGARCH"),
distribution.model = "norm")

spec = dccspec(uspec = multispec( replicate(3, uspec) ), VAR = TRUE,
lag = 1, dccOrder = c(1,1),  model = "DCC", distribution = "mvnorm")

fit = dccfit(spec, data = Data)

forecast = dccforecast(fit, n.ahead = 2, n.roll = 0)


And also the results:

> forecast@mforecast$mu , , 1 [,1] [,2] [,3] [1,] 1.339556 -1.828901 -3.290908 [2,] 1.331527 -1.814802 -3.290787 > var.predict$beta_1
fcst     lower    upper        CI
[1,] 1.339556 0.8548577 1.824255 0.4846984
[2,] 1.331527 0.6600307 2.003022 0.6714958

$beta_2 fcst lower upper CI [1,] -1.828901 -2.390441 -1.267361 0.5615401 [2,] -1.814802 -2.597114 -1.032490 0.7823119$beta_3
fcst     lower     upper       CI
[1,] -3.290908 -4.471721 -2.110096 1.180812
[2,] -3.290787 -4.871586 -1.709988 1.580799


• I thought rmgarch should be fine, but I cannot see any obvious mistakes in your code. And you say the package information suggests the estimation is simultaneous? Aug 16, 2018 at 10:23