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A test for constant correlations in a multivariate GARCH model. (English) Zbl 0968.62066

Summary: We introduce a Lagrange Multiplier (LM) test for the constant-correlation hypothesis in a multivariate GARCH model. The test examines the restrictions imposed on a model which encompasses the constant-correlation multivariate GARCH model. It requires the estimates of the constant-correlation model only and is computationally convenient. We report some Monte Carlo results on the finite-sample properties of the LM statistic. The LM test is compared against the Information Matrix (IM) test due to A.K. Bera and S. Kim [Testing constancy of correlation with an application to international equity returns. Mimeo (1996)]. The LM test appears to have good power against the alternatives considered and is more robust to nonnormality. We apply the test to three data sets, namely, spot-futures prices, foreign exchange rates and stock market returns. The results show that the spot futures and foreign exchange data have constant correlations, while the correlations across national stock market returns are time varying.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B28 Finance etc. (MSC2000)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62P20 Applications of statistics to economics
91B84 Economic time series analysis
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