This article is concerned with explosive AR(1) processes generated by conditionally heteroscedastic errors. Conditional least squares as well as generalized least squares estimation for autoregressive parameter are discussed and relevant limiting distributions are expressed as products of certain random variables. These results can be viewed as generalizations of classical results obtained for the standard explosive AR(1) model with i.i.d. errors(cf. Fuller(1996, Ch.10)). The model under consideration accommodates diverse conditionally heteroscedastic processes including Engle(1982)'s ARCH, threshold-ARCH(cf. Li and Li(1996)) and beta-ARCH processes(cf. Hwang and Basawa (2003)). Based on residuals, least squares estimation for parameters appearing in the conditional variance is also discussed and is illustrated for various ARCH type processes. A simulation study is conducted for comparing generalized least squares and conditional least squares estimation and it is seen that generalized least squares estimation performs better for simulated samples of moderate size.
Generalized Least Squares Estimation for Explosive AR(1) Processes with Conditionally Heteroscedastic Errors