Optimal Formulations for Nonlinear Autoregressive Processes

We develop optimal formulations for nonlinear autoregressive models by representing them as linear autoregressive models with time-varying temporal dependence coefficients. We propose a parameter updating scheme based on the score of the predictive likelihood function at each time point. The resulting time-varying autoregressive model is formulated as a nonlinear autoregressive model and is compared with threshold and smooth-transition autoregressive models. We establish the information theoretic optimality of the score driven nonlinear autoregressive process and the asymptotic theory for maximum likelihood parameter estimation. The performance of our model in extracting the time-varying or the nonlinear dependence for finite samples is studied in a Monte Carlo exercise. In our empirical study we present the in-sample and out-of-sample performances of our model for a weekly time series of unemployment insurance claims.