A Parsimonious Test of Constancy of a Positive Definite Correlation Matrix in a Multivariate Time-varying GARCH Model

Jian Kang; Johan Stax  Jakobsen; Annastiina Silvennoinen; Timo Teräsvirta; Glen Wade

doi:10.3390/econometrics10030030

A Parsimonious Test of Constancy of a Positive Definite Correlation Matrix in a Multivariate Time-varying GARCH Model

Jian Kang, Johan Stax Jakobsen, Annastiina Silvennoinen, Timo Teräsvirta^*, Glen Wade

^*Corresponding author for this work

Department of Finance

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

We construct a parsimonious test of constancy of the correlation matrix in the multivariate conditional correlation GARCH model, where the GARCH equations are time-varying. The alternative to constancy is that the correlations change deterministically as a function of time. The alternative is a covariance matrix, not a correlation matrix, so the test may be viewed as a general test of stability of a constant correlation matrix. The size of the test in finite samples is studied by simulation. An empirical example involving daily returns of 26 stocks included in the Dow Jones stock index is given.

Original language	English
Article number	30
Journal	Econometrics
Volume	10
Issue number	3
Number of pages	41
ISSN	2225-1146
DOIs	https://doi.org/10.3390/econometrics10030030
Publication status	Published - Sept 2022

Keywords

Deterministically varying correlation
Multiplicative time-varying GARCH
Multivariate GARCH
Nonstationary volatility
Smooth transition GARCH

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title = "A Parsimonious Test of Constancy of a Positive Definite Correlation Matrix in a Multivariate Time-varying GARCH Model",

abstract = "We construct a parsimonious test of constancy of the correlation matrix in the multivariate conditional correlation GARCH model, where the GARCH equations are time-varying. The alternative to constancy is that the correlations change deterministically as a function of time. The alternative is a covariance matrix, not a correlation matrix, so the test may be viewed as a general test of stability of a constant correlation matrix. The size of the test in finite samples is studied by simulation. An empirical example involving daily returns of 26 stocks included in the Dow Jones stock index is given.",

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T1 - A Parsimonious Test of Constancy of a Positive Definite Correlation Matrix in a Multivariate Time-varying GARCH Model

AU - Kang, Jian

AU - Jakobsen, Johan Stax

AU - Silvennoinen, Annastiina

AU - Teräsvirta, Timo

AU - Wade, Glen

PY - 2022/9

Y1 - 2022/9

N2 - We construct a parsimonious test of constancy of the correlation matrix in the multivariate conditional correlation GARCH model, where the GARCH equations are time-varying. The alternative to constancy is that the correlations change deterministically as a function of time. The alternative is a covariance matrix, not a correlation matrix, so the test may be viewed as a general test of stability of a constant correlation matrix. The size of the test in finite samples is studied by simulation. An empirical example involving daily returns of 26 stocks included in the Dow Jones stock index is given.

AB - We construct a parsimonious test of constancy of the correlation matrix in the multivariate conditional correlation GARCH model, where the GARCH equations are time-varying. The alternative to constancy is that the correlations change deterministically as a function of time. The alternative is a covariance matrix, not a correlation matrix, so the test may be viewed as a general test of stability of a constant correlation matrix. The size of the test in finite samples is studied by simulation. An empirical example involving daily returns of 26 stocks included in the Dow Jones stock index is given.

KW - Deterministically varying correlation

KW - Multiplicative time-varying GARCH

KW - Multivariate GARCH

KW - Nonstationary volatility

KW - Smooth transition GARCH

KW - Deterministically varying correlation

KW - Multiplicative time-varying GARCH

KW - Multivariate GARCH

KW - Nonstationary volatility

KW - Smooth transition GARCH

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DO - 10.3390/econometrics10030030

M3 - Journal article

SN - 2225-1146

VL - 10

JO - Econometrics

JF - Econometrics

IS - 3

M1 - 30

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