Local likelihood estimators in a regression model for stock returns

We consider a non-stationary regression-type model for stock returns in which the innovations are described by four-parameter distributions and the parameters are assumed to be smooth, deterministic functions of time. Also incorporating normal distributions for modelling the innovations, our model is capable of adapting to light-tailed innovations as well as to heavy-tailed innovations. Thus, it turns out to be a very flexible approach. For both the fitting of the model and for forecasting the distributions of future returns, we use local likelihood methods to estimate the parameters. We apply our model to the S&P 500 return series, observed over a period of 12 years. We show that it fits these data quite well and that it yields reasonable one-day-ahead forecasts.