Analysis of Poisson varying-coefficient models with autoregression

In the regression analysis of time series of event counts, it is of interest to account for serial dependence that is likely to be present among such data as well as a nonlinear interaction between the expected event counts and predictors as a function of some underlying variables. We thus develop a Poisson autoregressive varying-coefficient model, which introduces autocorrelation through a latent process and allows regression coefficients to nonparametrically vary as a function of the underlying variables. The nonparametric functions for varying regression coefficients are estimated with data-driven basis selection, thereby avoiding overfitting and adapting to curvature variation. An efficient posterior sampling scheme is devised to analyse the proposed model. The proposed methodology is illustrated using simulated data and daily homicide data in Cali, Colombia.