A note on limit theory for mildly stationary autoregression with a heavy-tailed GARCH error process

Abstract

A first-order mildly stationary autoregression with a heavy-tailed GARCH error process is considered to study the limit theory for the least squared estimator of the autoregression coefficient rho = rho(n) is an element of [0, 1). A Gaussian limit theory is established as rho(n) converges to the unity as n -> infinity, with rate condition (1 - rho(n))n -> infinity, as in Giraitis and Philips (2006), who have discussed the limit theory in case that errors are martingale difference sequences. This work addresses asymptotic results in a case of heavy-tailed GARCH errors, and extends the existing one by allowing errors to follow heavy-tailed process as well as conditional heteroscedasticity. (C) 2019 Elsevier B.V. All rights reserved.