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Strongly consistent model selection for general causal time series

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  • Kengne, William

Abstract

We consider the issue of strong consistency for model selection in a large class of causal time series models, including AR(∞), ARCH(∞), TARCH(∞), ARMA–GARCH and many other classical processes. We propose a penalized criterion based on the quasi likelihood of the model. We provide sufficient conditions that ensure the strong consistency of the proposed procedure. Also, the estimator of the parameter of the selected model obeys the law of iterated logarithm. It appears that, unlike the result of weak consistency obtained by Bardet et al. (2020), dependence between the regularization parameter and the model structure is not needed.

Suggested Citation

  • Kengne, William, 2021. "Strongly consistent model selection for general causal time series," Statistics & Probability Letters, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:stapro:v:171:y:2021:i:c:s0167715220303035
    DOI: 10.1016/j.spl.2020.109000
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    References listed on IDEAS

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    1. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    2. Jie Ding & Vahid Tarokh & Yuhong Yang, 2018. "Model Selection Techniques -- An Overview," Papers 1810.09583, arXiv.org.
    3. William Charky Kengne, 2012. "Testing for parameter constancy in general causal time‐series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 503-518, May.
    4. Bardet, Jean-Marc & Kengne, William, 2014. "Monitoring procedure for parameter change in causal time series," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 204-221.
    5. L. Zhao & C. Dorea & C. Gonçalves, 2001. "On Determination of the Order of a Markov Chain," Statistical Inference for Stochastic Processes, Springer, vol. 4(3), pages 273-282, October.
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    Cited by:

    1. William Kengne, 2023. "On consistency for time series model selection," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 437-458, July.
    2. Diop, Mamadou Lamine & Kengne, William, 2022. "Epidemic change-point detection in general causal time series," Statistics & Probability Letters, Elsevier, vol. 184(C).
    3. Mamadou Lamine Diop & William Kengne, 2025. "Statistical learning for $$\psi $$ ψ -weakly dependent processes," Statistical Inference for Stochastic Processes, Springer, vol. 28(2), pages 1-23, August.

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