MODEL SELECTION FOR INFINITE VARIANCE TIME-SERIES

In this study we consider the problem of model selection for infinite variance time series. We introduce a group of model selection criteria based on a general loss function Psi. This family includes various generalizations of predictive least square and AIC. Parameter estimation is carried out using Psi. We use two loss functions commonly used in robust estimation and show that certain criteria out perform the conventional approach based on least squares or Yule-Walker estimation for heavy tailed innovations. Our conclusions are based on a comprehensive study of the performance of competing criteria for a wide selection of AR(2) models. We also consider the performance of these techniques when the 'true' model is not contained in the family of candidate models.