A GQL estimation approach for analysing non-stationary over-dispersed BINAR(1) time series

ABSTRACT

This paper proposes a generalized quasi-likelihood (GQL) function for estimating the vector of regression and over-dispersion effects for the respective series in the bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with Negative Binomial (NB) marginals. The auto-covariance function in the proposed GQL is computed using some ‘robust’ working structures. As for the BINAR(1) process, the inter-relation between the series is induced mainly by the correlated NB innovations that are subject to different levels of over-dispersion. The performance of the GQL approach is tested via some Monte-Carlo simulations under different combination of over-dispersion together with low and high serial- and cross-correlation parameters. The model is also applied to analyse a real-life series of day and night accidents in Mauritius.

KEYWORDS:

• Non-stationary
• BINAR(1)
• GQL
• over-dispersion
• negative binomial

AMS SUBJECT CLASSIFICATION:

• 65C60
• 62J12
• 62H12
• 62J20
• 62J10

Acknowledgments

The authors are very grateful to the Statistics Mauritius and the Mauritius traffic branch for providing data on road traffic accidents in Mauritius.

Disclosure statement

No potential conflict of interest was reported by the authors.