A simple non-stationary model for stock returns

Abstract

The aim of the present peper is to show the example of the S&P 500 return series that a simple non-stationary model seem to fit the data significantly better than conventional GARCH-type models outperforming them also in forecasting the distribution of tomorrow's return. Instead of a complex endogenous specification of the conditional variance, we assume that the volatility dynamics is exogenous. Since no obvious canadidates explanatory exogenous variables are at hand, we model the volatility as deterministic. This approach leads to a structurally simple regression-type model. Special attention is paid to the accurate descripion of the tails of the innovations.