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

ArXiv ID: 2411.08246 “View on arXiv”

Authors: Unknown

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.

Keywords: Multivariate GARCH, DCC-GARCH, Eigenvalue Decomposition, Correlation Matrix Filtering, Out-of-sample Likelihood, Foreign Exchange (FX)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is highly mathematical, featuring advanced matrix theory (eigenvalue decomposition, covariance matrix adjustments), analytical derivations, and theoretical probability constructs, but its empirical evaluation is limited to a specific foreign exchange prediction task with basic likelihood metrics, lacking broader backtesting or implementation details.

  flowchart TD
    A["Research Goal: Improve DCC-GARCH Residual<br/>for FX Rate Prediction"] --> B["Methodology Formulation"]
    
    subgraph B ["Two Filtering Approaches"]
        B1["Approach 1: Correlation Matrix Estimation<br/>Transform Joint Distribution to Arbitrary Correlation"]
        B2["Approach 2: Eigenvalue Decomposition<br/>Transform Data to Uncorrelated Residuals"]
    end

    B --> C["Empirical Application"]
    
    subgraph C ["Data & Process"]
        C1["Input: Foreign Exchange Rates Dataset"]
        C2["Standard DCC-GARCH Model"]
        C1 --> C2
    end

    C2 --> D["Compute Residuals & Apply Filters"]
    D --> E["Evaluation & Comparison"]
    
    subgraph E ["Out-of-Sample Analysis"]
        E1["Prediction Task"]
        E2["Out-of-Sample Likelihood Metric"]
        E3["Comparison vs. Other Methodologies"]
    end

    E --> F["Key Findings"]
    
    subgraph F ["Outcomes"]
        F1["Proposed methods significantly improve<br/>DCC-GARCH residual independence"]
        F2["Enhanced prediction accuracy<br/>for foreign exchange rates"]
    end