Large sample inference for conditional exponential families with applications to nonlinear time series

Abstract

Let { Y t }, t =0, ±1, ±2,…, be a stationary ergodic Markov process taking values on the real line and such that the transition density function belongs to a conditional exponential family. In this paper, we establish the local asymptotic normality (LAN) of the log-likelihood ratio for this model. The LAN property leads to asymptotically optimal estimators and tests for the model parameters. The results are then applied to a class of nonlinear time series which includes viz. the random coefficient exponential and the random coefficient threshold autoregressive models.