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.
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