New approaches of the DCC-GARCH residual: Application to foreign exchange rates

Kenichiro Shiraya, Kanji Suzuki and Tomohisa Yamakami
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Kenichiro Shiraya: Graduate School of Economics, The University of Tokyo
Kanji Suzuki: Department of Mathematics, ETH Zurich. Department of Banking and Finance, University of Zurich
Tomohisa Yamakami: Graduate School of Economics, The University of Tokyo. Mizuho-DL Financial Technology Co., Ltd.

No CARF-F-592, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: Two formulations are proposed to filter out correlations in the residuals of the multivariate GARCH model. The first approach is to estimate the correlation matrix as a parameter and transform any joint distribution to have an arbitrary correlation matrix. The second approach transforms time series data into an uncorrelated residual based on the eigenvalue decomposition of a correlation matrix. The empirical performance of these methods is examined through a prediction task for foreign exchange rates and compared with other methodologies in terms of the out-of-sample likelihood. By using these approaches, the DCC-GARCH residual can be almost independent. This paper is available at https://arxiv.org/abs/2411.08246

Date: 2024-11
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