Comparison of specification tests for GARCH models

Kilani Ghoudi; Bruno Rémillard

doi:10.1016/j.csda.2013.03.009

Comparison of specification tests for GARCH models

Kilani Ghoudi, Bruno Rémillard

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

Specification procedures for testing the null hypothesis of a Gaussian distribution for the innovations of GARCH models are compared using simulations. More precisely, Cramér-von Mises and Kolmogorov-Smirnov type statistics are computed for empirical processes based on the standardized residuals and their squares. For calculating P-values, the parametric bootstrap method and the multipliers method are used. In addition, the Khmaladze transform is also applied to obtain an approximate Brownian motion under the null hypothesis, for which Cramér-von Mises and Kolmogorov-Smirnov type statistics are computed, using both the standardized residuals and their squares.

Original language	English
Pages (from-to)	291-300
Number of pages	10
Journal	Computational Statistics and Data Analysis
Volume	76
DOIs	https://doi.org/10.1016/j.csda.2013.03.009
Publication status	Published - Aug 2014

Keywords

Bootstrap
Empirical processes
GARCH models
Goodness of fit tests
Multipliers
Pseudo-observations
Residuals
Squared residuals

ASJC Scopus subject areas

Statistics and Probability
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.csda.2013.03.009

Cite this

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title = "Comparison of specification tests for GARCH models",

abstract = "Specification procedures for testing the null hypothesis of a Gaussian distribution for the innovations of GARCH models are compared using simulations. More precisely, Cram{\'e}r-von Mises and Kolmogorov-Smirnov type statistics are computed for empirical processes based on the standardized residuals and their squares. For calculating P-values, the parametric bootstrap method and the multipliers method are used. In addition, the Khmaladze transform is also applied to obtain an approximate Brownian motion under the null hypothesis, for which Cram{\'e}r-von Mises and Kolmogorov-Smirnov type statistics are computed, using both the standardized residuals and their squares.",

keywords = "Bootstrap, Empirical processes, GARCH models, Goodness of fit tests, Multipliers, Pseudo-observations, Residuals, Squared residuals",

author = "Kilani Ghoudi and Bruno R{\'e}millard",

note = "Funding Information: The authors appreciate the constructive remarks of the chief editor, the associate editor and two anonymous referees. Funding in partial support of this work was provided by the Natural Sciences and Engineering Research Council of Canada , the Fonds qu{\'e}b{\'e}cois de la recherche sur la nature et les technologies and the National Research Foundation of the United Arab Emirates . ",

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doi = "10.1016/j.csda.2013.03.009",

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AU - Ghoudi, Kilani

AU - Rémillard, Bruno

N1 - Funding Information: The authors appreciate the constructive remarks of the chief editor, the associate editor and two anonymous referees. Funding in partial support of this work was provided by the Natural Sciences and Engineering Research Council of Canada , the Fonds québécois de la recherche sur la nature et les technologies and the National Research Foundation of the United Arab Emirates .

PY - 2014/8

Y1 - 2014/8

N2 - Specification procedures for testing the null hypothesis of a Gaussian distribution for the innovations of GARCH models are compared using simulations. More precisely, Cramér-von Mises and Kolmogorov-Smirnov type statistics are computed for empirical processes based on the standardized residuals and their squares. For calculating P-values, the parametric bootstrap method and the multipliers method are used. In addition, the Khmaladze transform is also applied to obtain an approximate Brownian motion under the null hypothesis, for which Cramér-von Mises and Kolmogorov-Smirnov type statistics are computed, using both the standardized residuals and their squares.

AB - Specification procedures for testing the null hypothesis of a Gaussian distribution for the innovations of GARCH models are compared using simulations. More precisely, Cramér-von Mises and Kolmogorov-Smirnov type statistics are computed for empirical processes based on the standardized residuals and their squares. For calculating P-values, the parametric bootstrap method and the multipliers method are used. In addition, the Khmaladze transform is also applied to obtain an approximate Brownian motion under the null hypothesis, for which Cramér-von Mises and Kolmogorov-Smirnov type statistics are computed, using both the standardized residuals and their squares.

KW - Bootstrap

KW - Empirical processes

KW - GARCH models

KW - Goodness of fit tests

KW - Multipliers

KW - Pseudo-observations

KW - Residuals

KW - Squared residuals

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SP - 291

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JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

ER -

Comparison of specification tests for GARCH models

Abstract

Keywords

ASJC Scopus subject areas

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