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New approaches of the multivariate GARCH residual: application to foreign exchange rates

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  • Kenichiro Shiraya
  • Kanji Suzuki
  • Tomohisa Yamakami

Abstract

Two formulations are proposed to filter out correlations in the residuals of the multivariate GARCH model. The first approach estimates the correlation matrix as a parameter and transforms any joint distribution to match a specific correlation matrix. The second approach converts time series data into an uncorrelated residuals using the eigenvalue decomposition of the correlation matrix. The empirical performance of these methods is evaluated through a prediction task involving foreign exchange rates and is compared with other methodologies based on out-of-sample log-likelihood and Value at Risk. These approaches approximate the DCC-GARCH residuals with independent factors, thereby avoiding the modeling of complex higher-order dependencies.

Suggested Citation

  • Kenichiro Shiraya & Kanji Suzuki & Tomohisa Yamakami, 2025. "New approaches of the multivariate GARCH residual: application to foreign exchange rates," Quantitative Finance, Taylor & Francis Journals, vol. 25(9), pages 1461-1483, September.
    • Handle: RePEc:taf:quantf:v:25:y:2025:i:9:p:1461-1483
    DOI: 10.1080/14697688.2025.2547829
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