Dependent and Independent Time Series Errors Under Elliptically Countered Models

Fredy O. Pérez-Ramirez (), Francisco J. Caro-Lopera, José A. Díaz-García and Graciela González Farías
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Fredy O. Pérez-Ramirez: Faculty of Engineering, University of Medellin, Medellin 050026, Colombia
Francisco J. Caro-Lopera: Faculty of Basic Sciences, University of Medellin, Medellin 050026, Colombia
José A. Díaz-García: Facultad de Zootecnia y Ecología, Universidad Autónoma de Chihuahua, Chihuahua 31453, Mexico
Graciela González Farías: Instituto de Ciencia de los Datos e Inteligencia Artificial (DATAI), 31009 Pamplona, Spain

Econometrics, 2025, vol. 13, issue 2, 1-26

Abstract: We explore the impact of time series behavior on model errors when working under an elliptically contoured distribution. By adopting a time series approach aligned with the realistic dependence between errors under such distributions, this perspective shifts the focus from increasingly complex and challenging correlation analyses to volatility modeling that utilizes a novel likelihood framework based on dependent probabilistic samples. With the introduction of a modified Bayesian Information Criterion, which incorporates a ranking of degrees of evidence of significant differences between the compared models, the critical issue of model selection is reinforced, clarifying the relationships among the most common information criteria and revealing limited relevance among the models based on independent probabilistic samples, when tested on a well-established database. Our approach challenges the traditional hierarchical models commonly used in time series analysis, which assume independent errors. The application of rigorous differentiation criteria under this novel perspective on likelihood, based on dependent probabilistic samples, provides a new viewpoint on likelihood that arises naturally in the context of finance, adding a novel result. We provide new results for criterion selection, evidence invariance, and transitions between volatility models and heuristic methods to calibrate nested or non-nested models via convergence properties in a distribution.

Keywords: time series; volatility models; elliptically contoured models; selection criteria; grades of evidence for significant difference; ARCH; GARCH; TGARCH; EGARCH models (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2025
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