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On Some Non-stationary Bivariate INAR(p) Models with Applications to Intra-day Stock Transaction Series

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Abstract

This paper introduces a non-stationary bivariate integer-valued auto-regressive process of order p (BINAR(p) with non-stationary moments. The BINAR(p) uses the conventional binomial thinning procedure and the cross correlation between the two related series is induced from the paired innovation terms. The conditional maximum likelihood (CML) approach is used to estimate the model parameters. Monte Carlo simulation experiments with bivariate Poisson innovations are implemented to assess the consistency and asymptotic properties of the proposed BINAR(p). In the application part, we consider two bivariate time series: The Ask and bid quotes from AT &T and the intra-day transactions of Mauritius Commercial Bank (MCB) and State Bank of Mauritius Holdings (SBMH). These series were fitted using the BINAR(p) with paired Poisson, Negative Binomial and Poisson-Lindley innovations and the results demonstrate that BINAR(p) with Negative Binomial yield better fitting and slightly lesser mean square error.

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Acknowledgements

This work is also part of my Post-Doctoral Fellowship on “The Family of Bivariate Integer-Valued Autoregressive Models” at the University of Bahia, Brazil. I am thankful to Prof. Paulo Jorge Canas Rodrigues and to the anonymous reviewers for their suggestions.

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No funding was received for this research work.

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Authors and Affiliations

  1. University of Technology Mauritius, Pointe-Aux-Sables, Mauritius

    Y. Sunecher

  2. University of Mauritius, Reduit, Mauritius

    N. Mamode Khan & V. Jowaheer

  3. Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia

    Hassan S. Bakouch

  4. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

    Hassan S. Bakouch

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  1. Y. Sunecher
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  2. N. Mamode Khan
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  3. Hassan S. Bakouch
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  4. V. Jowaheer
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Correspondence to Y. Sunecher.

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Sunecher, Y., Mamode Khan, N., Bakouch, H.S. et al. On Some Non-stationary Bivariate INAR(p) Models with Applications to Intra-day Stock Transaction Series. J Indian Soc Probab Stat (2024). https://doi.org/10.1007/s41096-024-00177-w

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