Semiparametric Regression for Time Series of Counts

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 {epsilon(t)}. The conditional mean ut of the response variable given {epsilon(t)} is of the form u(t) = exp[beta X-T(t) + eta(Z(t))]epsilon(t), where X-t and Z(t) are covariates at time t, beta is an unknown parameter vector, and eta(center dot) is an unknown smooth function. We use non parametric kernel estimating equations to estimate the function eta(center dot) and profile-based estimating equations to estimate the parameter vector beta. We derive the asymptotic properties of the estimators, and conduct simulation studies to evaluate the finite sample performance of the estimation procedure.