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Density Power Divergence Estimator for General Integer-Valued Time Series with Exogenous Covariates

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Abstract

In this article, we study a robust estimation method for a general class of integer-valued time series models. The conditional distribution of the process belongs to a broad class of distributions and unlike the classical autoregressive framework, the conditional mean of the process also depends on some exogenous covariates. We derive a robust inference procedure based on the minimum density power divergence. Under certain regularity conditions, we establish that the proposed estimator is consistent and asymptotically normal. In the case where the conditional distribution belongs to the exponential family, we provide sufficient conditions for the existence of a stationary and ergodic \(\tau \)-weakly dependent solution. Simulation experiments are conducted to illustrate the empirical performances of the estimator. An application to the number of transactions per minute for the stock Ericsson B is also provided.

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Acknowledgements

The authors are grateful to the two anonymous Referees for many relevant suggestions and comments which helped to improve the contents of this paper.

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Authors and Affiliations

  1. THEMA, CY Cergy Paris Université, 33 Boulevard du Port, 95011, Cergy-Pontoise Cedex, France

    Mamadou Lamine Diop & William Kengne

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  1. Mamadou Lamine Diop
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  2. William Kengne
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Correspondence to William Kengne.

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The authors have no conflicts of interest to declare that are relevant to the content of this article.

Additional information

Mamadou Lamine Diop supported by the MME-DII center of excellence (ANR-11-LABEX-0023-01) and the ANR BREAKRISK: ANR-17-CE26-0001-01.

William Kengne developed within the CY Initiative of Excellence (grant “Investissements d’Avenir” ANR-16-IDEX-0008), Project “EcoDep” PSI-AAP2020-0000000013.

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Diop, M.L., Kengne, W. Density Power Divergence Estimator for General Integer-Valued Time Series with Exogenous Covariates. Commun. Math. Stat. (2023). https://doi.org/10.1007/s40304-023-00351-9

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  • DOI: https://doi.org/10.1007/s40304-023-00351-9

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