Asymptotic optimal inference for a class of nonlinear time series models

Abstract

The local asymptotic normality (LAN) of the log-likelihood ratio for a class of Markovian nonlinear time series models is established using the approach of quadratic mean differentiability. The error process in the models considered is not necessarily Gaussian. As a consequence of the LAN property, asymptotically optimal estimators of the model parameters are derived. Also, asymptotically efficient tests for linearity are constructed. Several examples are discussed as special cases.