Local quasi-likelihood approach to varying-coefficient discrete-valued time series models

Abstract

This article develops a local linear quasi-likelihood approach to regression analysis with discrete-valued time series data. A class of nonlinear time series models—varying-coefficient models is considered, which include the parametric Markov regression models for time series as special cases, proposed and studied by Zeger and Qaqish [Zeger, S. L. and Qaqish, B. (1988). Markov regression models for time series: a quasi-likelihood approach. Biometrics, 44, 1019–1031.]. The local linear fitting is proposed to estimate the coefficient functions and the asymptotic property of the resulting estimator is studied. Also proposed are a nonparametric version of Akaike information criterion to select the bandwidth, and an empirical method to derive the estimate of covariance. A small simulated example and a real data set for respiratory disease are used to illustrate the methodology.