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

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

pvestia
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


Thanks you very much.

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