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Statistical Methods & Applications

, Volume 28, Issue 4, pp 625–653 | Cite as

BINAR(1) negative binomial model for bivariate non-stationary time series with different over-dispersion indices

  • Yuvraj SunecherEmail author
  • Naushad Mamode Khan
  • Miroslav M. Ristić
  • Vandna Jowaheer
Original Paper

Abstract

The existing stationary bivariate integer-valued autoregressive model of order 1 (BINAR(1)) with correlated Negative Binomial (NB) innovations is capable of modelling stationary count series where the innovation terms of both series have same over-dispersion index. Such BINAR(1) may not be useful to model real-life series that are affected by common time-dependent covariates whereby the two series may display non-stationarity as well as different over-dispersion indices. In this paper, we propose a novel BINAR(1) model with the pair of innovations following a joint NB distribution that accommodates different over-dispersion indices. The estimation of parameters is conducted using generalized quasi-likelihood (GQL) approach that operates in two phases. Monte Carlo simulations are implemented to assess the performance of the proposed GQL under the wide range of combinations of the model parameters. This BINAR(1) model is also applied to analyze the daily series of day and night accident data in some regions of Mauritius.

Keywords

BINAR(1) Non-stationary NB GQL Over-dispersion 

Mathematics Subject Classification

65C60 62J12 62H12 62J20 62J10 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yuvraj Sunecher
    • 1
    Email author
  • Naushad Mamode Khan
    • 2
  • Miroslav M. Ristić
    • 3
  • Vandna Jowaheer
    • 2
  1. 1.University of Technology MauritiusPort LouisMauritius
  2. 2.University of MauritiusReduitMauritius
  3. 3.University of NišNišSerbia

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