![]() The first application uses the model as an alternative for handling outliers in time series analysis. Finally, two applications of the proposed model are considered. The information criterion approach is adopted to specify the order of the transfer function equation, and simulation is used to illustrate the performance of the criteria, for example, Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). Properties of the proposed general models are discussed, and a model specification procedure is suggested. The use of a purely random coefficient transfer function model to describe the varying conditional variance is based on the fact that the relationship between the conditional variance and available information must be unidirectional. In addition, the proposed model also allows for the conditional variance to be a function of the square of the conditional expectation. Both the RCA and the ARCH models become special cases of this general model. The second goal of this article is, therefore, to propose a general class of conditional heteroscedastic time series models, each of which consists of a constant coefficient autoregressive moving average (ARMA) model and a purely random coefficient transfer function model. This recognition immediately points out that to describe the varying conditional variance the RCA and ARCH models may not be parsimonious in parametrization and further extension is needed. The RCA models allow for the conditional variance to evolve with previous observations, whereas the ARCH models make use of previous innovations. This feature is presented in two ways from which the two models differ. In this article, I first give the relationship between these two types of models and show that the special feature of these two models is the varying conditional variance. The interesting fact is that the ARCH processes can be regarded as special cases of the RCA model. 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. 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. Experience in conjunction with data analysis, however, suggests that the variability of a process might well depend on the available information. Under the traditional linear time series or regression setting, the conditional variance of one-step-ahead prediction is time invariant. ![]()
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