Optimal Neighborhood Selection for AR-ARCH Random Fields with Application to Mortality

Paul Doukhan, Joseph Rynkiewicz and Yahia Salhi
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Paul Doukhan: UMR 8088 Analyse, Géométrie et Modélisation, Université de Cergy-Pontoise, 2, Avenue Adolphe Chauvin, CEDEX, 95302 Cergy-Pontoise, France
Joseph Rynkiewicz: Équipe SAMM, EA 4543, Université Paris I Panthéon-Sorbonne 90, Rue de Tolbiac, CEDEX 13, 75634 Paris, France
Yahia Salhi: ISFA, LSAF EA2429, Univ Lyon, Université Lyon 1, 50 Avenue Tony Garnier, 69007 Lyon, France

Stats, 2021, vol. 5, issue 1, 1-26

Abstract: This article proposes an optimal and robust methodology for model selection. The model of interest is a parsimonious alternative framework for modeling the stochastic dynamics of mortality improvement rates introduced recently in the literature. The approach models mortality improvements using a random field specification with a given causal structure instead of the commonly used factor-based decomposition framework. It captures some well-documented stylized facts of mortality behavior including: dependencies among adjacent cohorts, the cohort effects, cross-generation correlations, and the conditional heteroskedasticity of mortality. Such a class of models is a generalization of the now widely used AR-ARCH models for univariate processes. A the framework is general, it was investigated and illustrated a simple variant called the three-level memory model. However, it is not clear which is the best parameterization to use for specific mortality uses. In this paper, we investigate the optimal model choice and parameter selection among potential and candidate models. More formally, we propose a methodology well-suited to such a random field able to select thebest model in the sense that the model is not only correct but also most economical among all thecorrectmodels. Formally, we show that a criterion based on a penalization of the log-likelihood, e.g., the using of the Bayesian Information Criterion, is consistent. Finally, we investigate the methodology based on Monte-Carlo experiments as well as real-world datasets.

Keywords: mortality rates; AR-ARCH random field; estimation; model selection; BIC (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2021
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