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Copula-Based Dynamic Conditional Correlation Multiplicative Error Processes

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  • Taras Bodnar
  • Nikolaus Hautsch

Abstract

We introduce a copula-based dynamic model for multivariate processes of (non-negative) high-frequency trading variables revealing time-varying conditional variances and correlations. Modeling the variables’ conditional mean processes using a multiplicative error model we map the resulting residuals into a Gaussian domain using a Gaussian copula. Based on high-frequency volatility, cumulative trading volumes, trade counts and market depth of various stocks traded at the NYSE, we show that the proposed copula-based transformation is supported by the data and allows disentangling (multivariate) dynamics in higher order moments. To capture the latter, we propose a DCC-GARCH specification. We suggest estimating the model by composite maximum likelihood which is sufficiently flexible to be applicable in high dimensions. Strong empirical evidence for time-varying conditional (co-)variances in trading processes supports the usefulness of the approach. Taking these higher-order dynamics explicitly into account significantly improves the goodness-of-fit of the multiplicative error model and allows capturing time-varying liquidity risks.

Suggested Citation

  • Taras Bodnar & Nikolaus Hautsch, 2012. "Copula-Based Dynamic Conditional Correlation Multiplicative Error Processes," SFB 649 Discussion Papers SFB649DP2012-044, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2012-044
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    1. Nikolaus Hautsch & Ostap Okhrin & Alexander Ristig, 2014. "Efficient Iterative Maximum Likelihood Estimation of High-Parameterized Time Series Models," SFB 649 Discussion Papers SFB649DP2014-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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    More about this item

    Keywords

    multiplicative error model; trading processes; copula; DCC-GARCH; liquidity risk;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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