Estimation of VAR(1)-GARCH(1,1) model

[TomDoan]

OK. One forecasts variance H1. The other forecasts variance H2. Which is better and why?

[irfanawan]

Dear Tom,

I estimate Bivariate MGARCH model two times. One for raw returns and other for adjusted returns. I wants to compare forecast performance of model of variance ( H1 and H2). As it is not possible to forecast from VAR-GARCH model. Is it possible to forecast variance using other multivariate GARCH model.

Regards

[TomDoan]

First of all, you're missing the point. Suppose you have a way to forecast the variances. Then what? You have yet to describe what you will do with those to compare "forecast performance". Also, is there any real point to showing that it's easier to forecast clean data than dirty data?

[irfanawan]

Dear Tom,
I want to compare the forecast performance of same model using Raw data and cleaned data. Let suppose that I have two stocks (SP500 and FTSE100) returns and I estimated bivariate GARCH model for both Raw and Cleaned data. I want to forecast conditional variance of both stocks and wants to test there is any improvement in variance forecast for outliers corrected data. Suppose I estimated the model using daily data from January 2010 to December 2015 and left data for two months to compare forecast. I will use Mean absolute error, median or any other measure for this purpose. Now what should I do to get forecasts of conditional variance of both stock for two months? If I have estimated VAR-GARCH model.

Regards
Irfan

[TomDoan]

How do you plan to compute the MAE? The variance that the GARCH model is forecasting isn't observable. (If it were observable, you wouldn't be doing GARCH models).

And again, why is it interesting to see whether it's easier to forecast outlier-adjusted data than raw data? Of course it is.

[irfanawan]

Dear Tom,
I will calculate MAE using the difference between forecast variance and squared of returns. I just want to check the correction of outliers makes forecast more accurate than outliers contaminated series.

Regards

[TomDoan]

1. It wouldn't be the squared returns, it would be the squared one-step-ahead forecast errors.
2. Squared errors aren't very useful for evaluating GARCH models. See Andersen and Bollerslev(1998), "Answering the skeptics: Yes, standard volatility models do provide accurate forecasts." International Economic Review.
3. MAE's on the squared errors, in particular, are a very bad way to evaluate GARCH models. Even if the model exactly hits the true volatility, the MAE will be lower for a competing model which (significantly) underestimates the volatility. (E|Z-x| is minimized for x=median of Z, which, when Z is the squared errors, is quite a bit lower than the mean).
4. I don't know anyone who has claimed that 60 step out GARCH model forecasts are at all useful for anything. In general, variances are only a useful summary for a distribution which is at least approximately Normal and (unconditional) GARCH process errors are anything but.
5. And again, why would it be at all interesting to discover that it's easier to forecast clean data than dirty data?