GARCH Toolbox

Computing Root Mean Square Errors (RMSE)

You can also use garchpred to calculate the root mean square errors (RMSE) associated with the conditional mean forecasts in yFcast.

• [sFcast, yFcast, sTotal, yRMSE]  = garchpred(coeff, xyz, 10);
  [yFcast, yRMSE]
  ans =
    4.9183e-004  1.1670e-002
    4.9183e-004  1.1674e-002
    4.9183e-004  1.1678e-002
    4.9183e-004  1.1682e-002
    4.9183e-004  1.1686e-002
    4.9183e-004  1.1690e-002
    4.9183e-004  1.1694e-002
    4.9183e-004  1.1697e-002
    4.9183e-004  1.1701e-002
    4.9183e-004  1.1705e-002
  

The first column above contains the minimum mean square error (MMSE) forecasts of the conditional mean of the returns in each of the first 10 periods (from the section Forecasting Over a Longer Horizon). The second column contains the standard error of the corresponding forecast (see Baillie & Bollerslev [1], equation 19, page 96). You can use these results to construct approximate confidence intervals for conditional mean forecasts, with the approximation becoming more accurate during periods of relatively stable volatility (see Baillie & Bollerslev [1], and Bollerslev, Engle, and Nelson [6]). As heteroscedasticity in returns disappears (i.e., as the returns approach the homoskedastic, or constant variance, limit), the approximation is exact and you can apply the Box & Jenkins confidence bounds (see Box, Jenkins, and Reinsel [7], pages 133-145).

Note    The yRMSE output of garchpred is not available for conditional mean models with regression components.

Computing a Forecast

Asymptotic Behavior for Long-Range Forecast Horizons