Strongly consistent model selection for general causal time series

William Kengne

Statistics & Probability Letters, 2021, vol. 171, issue C

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.

Keywords: Model selection; Strong consistency; Causal processes; Quasi-maximum likelihood estimation; Penalized contrast (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2020.109000

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