A semi‐parametric integer‐valued autoregressive model with covariates

We consider a low count data INAR (Integer Autoregressive Regression) model in which the arrivals are modelled non‐parametrically and are allowed to contain covariates. Accommodating possible covariates is important as exogenous variability, such as seasonality, often needs to be catered for. The main challenge is to maintain the axiomatic properties of the arrivals non‐parametric mass function while, at the same time, incorporating covariates directly into the associated probabilities. Compared with models that impose standard distributions such as Poisson or Negative Binomial for the arrivals, our approach is more flexible and provides a general arrival specification. The dependence structure is parametric and uses the standard binomial thinning operator. The parameters are estimated by the Maximum Likelihood. Monte Carlo simulations show that our proposed model performs very well with good finite sample results. Two empirical issues are addressed where incorporating covariates is a prerequisite for successful modelling. The first incorporates seasonal covariates into a semi‐parametric model for forecasting the numbers of claimants of wage loss benefits in the logging industry in British Columbia, Canada. The second investigates if macro‐economic indicators in an economy may be useful in predicting the number of bank failures in the US financial sector.