Time Dependence and Moments of a Family of Time-Varying Parameter Garch in Mean Models

In this paper we consider the time series dependence, stationarity, and higher moments issues of a family of first-order conditionally heteroskedastic in mean models with a possibly time-varying mean parameter. The interest in these models lies in the fact that economic theory and physics often require the connection between the first and second conditional moments of time series. Our results reveal important properties of these models, which are consistent with stylized facts in financial and turbulence data sets. They can also be employed for model identification, estimation, and testing. Copyright 2004 Blackwell Publishing Ltd.