GARCH Toolbox

Asymptotic Behavior for Long-Range Forecast Horizons

If you are working with long-range forecast horizons, the following asymptotic behaviors hold for the outputs of garchpred:

• As mentioned earlier in this section, the conditional standard deviation forecast (i.e., the first garchpred output, sFcast) approaches the unconditional standard deviation of {_t} given by the square root of Eq. (2-7).
• GARCH effects do not affect the MMSE forecast of the conditional mean (i.e., the second garchpred output, yFcast). The forecast approaches the unconditional mean of {y_t} as in the constant variance case. That is, the presence of GARCH effects introduces dependence in the variance process, and only affects the uncertainty of the mean forecast, leaving the mean forecast itself unchanged.
• The mean-square-error of the conditional mean (i.e., the square of the fourth garchpred output, yRMSE.^2) approaches the unconditional variance of {y_t}.

Computing Root Mean Square Errors (RMSE)

Conditional Mean Models with Regression Components