Semiparametric Regression for Time Series of Counts

Qin Wang and Rongning Wu

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 5, 983-995

Abstract: We study estimation in a parameter-driven semiparametric regression model for time series of counts, where serial dependence among the observed counts is introduced by an autocorrelated latent process {ϵt}. The conditional mean ut of the response variable given {ϵt} is of the form ut=exp[βTXt+η(Zt)]ϵt$u_{t}=\exp [\pmb {\beta }^T{\mathbf {X}}_{t}+\eta (Z_{t})]\varepsilon _{t}$, where Xt and Zt are covariates at time t, β$\pmb {\beta }$ is an unknown parameter vector, and η( · ) is an unknown smooth function. We use non parametric kernel estimating equations to estimate the function η( · ) and profile-based estimating equations to estimate the parameter vector β$\pmb {\beta }$. We derive the asymptotic properties of the estimators, and conduct simulation studies to evaluate the finite sample performance of the estimation procedure.

Date: 2015
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DOI: 10.1080/03610926.2012.750359

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