First-Order Autoregressive Processes with Heterogeneous Persistence

We propose a semi-nonparametric method of identification and estimation for Gaussian autoregressive processes with stochastic autoregressive coefficients. The autoregressive coefficient is considered as a latent process with either a moving average or regime switching representation. We develop a consistent estimator of the distribution of the autoregressive coefficient based on nonlinear canonical decomposition of the observed process. The approach is illustrated by simulations. Copyright 2003 Blackwell Publishing Ltd.