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) ##


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) ##


 uspec = ugarchspec(mean.model = list(armaOrder = c(0,0), include.mean = 
                    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
         fcst     lower    upper        CI
[1,] 1.339556 0.8548577 1.824255 0.4846984
[2,] 1.331527 0.6600307 2.003022 0.6714958

          fcst     lower     upper        CI
[1,] -1.828901 -2.390441 -1.267361 0.5615401
[2,] -1.814802 -2.597114 -1.032490 0.7823119

          fcst     lower     upper       CI
[1,] -3.290908 -4.471721 -2.110096 1.180812
[2,] -3.290787 -4.871586 -1.709988 1.580799

1 Answer 1


If the model is estimated in stages (conditional mean equations first, conditional variance equations second), the conditional variance specification will not affect estimates of the parameters in the conditional mean model. Then point forecasts equal to predicted conditional mean will not be affected. Interval forecasts, however, will be affected since the spread around the conditional mean will vary depending on the conditional variance model. Other types of point forecasts such as predicted quantiles will also be affected by that.

If the model is estimated in one stage (both the conditional mean and variance equations together), even the point forecasts should differ from a model with constant conditional variance specification -- unless the effects of the nonconstant conditional variance on the estimates of the parameters in the conditional mean equation happen to cancel out exactly (which is very unlikely).

  • $\begingroup$ Thank you Richard, after read the package I believe they should be estimated in one stage. I will add to my question, the code of me forecasting with VAR-GARCH and VAR. Obtaining the same result, perhaps is something wrong with my scrip. I will add a question to this comment: Do you know any statisticall or econometric software that performs an one stage VAR-GARCH and its possible to perform a forecast? $\endgroup$
    – pvestia
    Aug 16, 2018 at 10:08
  • $\begingroup$ I already uploaded the code to the question, can you give it a look please? It would be extremely appreciated. $\endgroup$
    – pvestia
    Aug 16, 2018 at 10:22
  • $\begingroup$ 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? $\endgroup$ Aug 16, 2018 at 10:23
  • $\begingroup$ Richard do you know any software where is possible to perform one step VAR-GARCH? I do believe the GARCH in the rmgarch is modeled in a second moment. $\endgroup$
    – pvestia
    Aug 18, 2018 at 12:20
  • $\begingroup$ @PauloVéstia, sorry, I don't know. $\endgroup$ Aug 18, 2018 at 15:06

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