On the Independence of the Standardized One-Step-Ahead Prediction Errors in Arch Models

Proceedings of the 7th Hellenic-European Conference on Computer Mathematics and its Applications, 2005

9 Pages Posted: 6 Feb 2008 Last revised: 23 Jan 2009

See all articles by Stavros Antonios Degiannakis

Stavros Antonios Degiannakis

Department of Economic and Regional Development, Panteion University of Political and Social Sciences

Evdokia Xekalaki

Athens University of Economics and Business

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Abstract

In statistical modeling contexts, the use of one-step-ahead prediction errors for testing hypotheses on the forecasting ability of an assumed model has been widely considered (see, e.g. Xekalaki et al. (2003, in Stochastic Musings, J.Panaretos (ed.), Laurence Erlbaum), Degiannakis and Xekalaki (2005, Journal of Applied Stochastic Models in Business and Industry). Quite often, the testing procedure requires independence in a sequence of recursive standardized prediction errors, which cannot always be readily deduced particularly in the case of econometric modeling. In this paper, the results of a series of Monte Carlo simulations reveal that independence can be assumed to hold. They are also indicative of a chi-square distribution for the sum of squared standardized one step- ahead prediction errors. Some theoretical justification of these findings can be traced in Degiannakis and Xekalaki's results (2005, Journal of Applied Stochastic Models in Business and Industry).

Keywords: ARCH models, Standardized Prediction Error Criterion, Model selection, Monte Carlo Simulation, Predictability, One-step-ahead Prediction Errors

Suggested Citation

Degiannakis, Stavros Antonios and Xekalaki, Evdokia, On the Independence of the Standardized One-Step-Ahead Prediction Errors in Arch Models. Proceedings of the 7th Hellenic-European Conference on Computer Mathematics and its Applications, 2005, Available at SSRN: https://ssrn.com/abstract=1087983

Stavros Antonios Degiannakis

Department of Economic and Regional Development, Panteion University of Political and Social Sciences ( email )

136 Sygrou
Athens
Greece

Evdokia Xekalaki (Contact Author)

Athens University of Economics and Business ( email )

76 Patission Street
GR-10434 Athens
Greece

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