Conditional Heteroscedastic Time Series Models

Abstract

Abstract Under the traditional linear time series or regression setting, the conditional variance of one-step-ahead prediction is time invariant. Experience in conjunction with data analysis, however, suggests that the variability of a process might well depend on the available information. This reality has motivated extensive research to relax the constant variance assumption imposed by the traditional linear time series model, and several classes of generalized parametric models designed specifically for handling nonhomogeneity of a process have been proposed recently. In particular, the random coefficient autoregressive (RCA) models were widely investigated by time series analysts and the autoregressive conditional heteroscedastic (ARCH) models were investigated by econometricians. The interesting fact is that the ARCH processes can be regarded as special cases of the RCA model. In this article, I first give the relationship between these two types of models and show that the special feature of these t...