Variations in returns/volatility and persistence in variance. An application to the Spanish stock market

A methodology is proposed to select the information set in ARMA-GARCH models in order to forecast the future evolution of an univariate heteroscedastic time series when it is suspected that the DGP is time changing. Using this methodology the stability of the DGP in the Spanish Stock Market is analysed. In this case it is shown that the DGP is time-varying and, in particular, the persistence in variance is over-valued using classical methods. Furthermore, the predictive intervals obtained have better coverage properties, by more adequately reflecting the uncertainty associated to the evolution of the time series being analysed.