Strong consistent model selection for general causal time series

2020/08/20 by William Kengne, Kengne, William
Computer Science · Economics, Econometrics and Finance · Mathematics · #Blind Source Separation Techniques #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2008.08778

openalex publication_date 2020/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the strongly consistent question for model selection in a large class of causal time series models, including AR(∞), ARCH(∞), TARCH(∞), ARMA-GARCH and many classical others 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 the weak consistency obtained by Bardet \it et al. \citeBardet2020, a dependence between the regularization parameter and the model structure is not needed.

Citations

• The Estimation of the Order of an ARMA Process

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