Asymptotically optimal tests for non-linear autoregressive model with [formula omitted]-ARCH errors

Abstract

This paper develops optimal statistical tests for testing certain class of non-linear time series models contiguous to a non-linear autoregressive processes with β-ARCH errors. The statistical tests are based on the Local Asymptotic Normality -LAN-(established via the quadratic mean differentiability) of the log-likelihood ratio of the studied Model when its parameters are estimated. Their local power are also computed. Some examples related to financial models are considered. Our approach uses mainly an efficient estimators of Bouzebda and Lounis (2019).