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

TL;DR

This paper introduces two novel methods for filtering correlations in DCC-GARCH residuals, enhancing their independence, and demonstrates their effectiveness in foreign exchange rate prediction tasks.

Contribution

It proposes two new formulations for residual correlation filtering in DCC-GARCH models, improving residual independence in financial data analysis.

Findings

Residuals become nearly independent using proposed methods

Enhanced out-of-sample likelihood in foreign exchange prediction

Methods outperform existing correlation filtering techniques

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.