GARCH Toolbox

Generating Forecasted Explanatory Data

Typically, the regression matrix X contains the observed returns of a suitable market index, collected over the same time interval as the observed data of interest. In this case, X is most likely a vector, corresponding to a single explanatory variable, and you must devise some way of generating the forecast of X (i.e., XF).

One approach, using the GARCH Toolbox, is to first use garchfit to fit a suitable ARMA(R,M) model to the returns in X, then use garchpred to forecast the market index returns into the future. Specifically, since you're not interested in fitting the volatility of X, you can simplify the estimation process by assuming a constant conditional variance model, e.g., ARMA(R,M)/GARCH(0,0).

Forecasted Explanatory Data

Ordinary Least Squares Regression