Inference for the Non-Stationary First Order Integer-Valued Moving Average (INMA(1)) Process with COM-Poisson Innovations

SYNOPTIC ABSTRACT

This article proposes a first order integer-valued moving average (INMA(1)) process where the innovations are COM-Poisson under non-stationary moments. In this set-up, the non-stationary is induced through time-dependent covariates. However, the corresponding marginal distribution of the counting series is rather difficult to specify and, hence, this limits the application of likelihood-based approachers to estimate the model parameters. In this context, a generalized quasi-likelihood (GQL) approach is developed to estimate the different effects. Monte-Carlo simulations are implemented to assess the consistency of the GQL estimators. A small application on road accident series is conducted via the proposed INMA(1) model.

KEY WORDS AND PHRASES:

• COM-Poisson
• dispersion
• GQL
• INMA
• non-stationary