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

• Published in: Journal of statistical computation and simulation Vol. 87; no. 10; pp. 1911 - 1924
• Main Authors: Sunecher, Yuvraj, Khan, Naushad Mamode, Jowaheer, Vandna
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.07.2017; Taylor & Francis Ltd
• Subjects: Autoregressive processes; BINAR; Bivariate analysis; Computer simulation; Covariance; Dispersion; GQL; Monte Carlo simulation; negative binomial; Non-stationary; over-dispersion; Regression analysis; Series (mathematics)
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2017.1296152

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.