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Volatility Comovement: a multifrequency approach

Author

Listed:
  • Laurent-Emmanuel Calvet

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Adlai J. Fisher
  • Samuel B. Thompson

Abstract

We implement a multifrequency volatility decomposition of three exchange rates and show that components with similar durations are strongly correlated across series. This motivates a bivariate extension of the Markov-Switching Multifractal (MSM) introduced in Calvet and Fisher (J. Econ. 105 (2001) 27, J. Financ. Econ. 2 (2004) 49). Bivariate MSM is a stochastic volatility model with a closed-form likelihood. Estimation can proceed by maximum likelihood for state spaces of moderate size, and by simulated likelihood via a particle filter in high-dimensional cases. We estimate the model and confirm its main assumptions in likelihood ratio tests. Bivariate MSM compares favorably to a standard multivariate GARCH both in- and out-of-sample. A parsimonious multifrequency factor structure is finally proposed for multivariate settings with potentially many assets.

Suggested Citation

  • Laurent-Emmanuel Calvet & Adlai J. Fisher & Samuel B. Thompson, 2006. "Volatility Comovement: a multifrequency approach," Post-Print hal-00459667, HAL.
  • Handle: RePEc:hal:journl:hal-00459667
    DOI: 10.1016/j.jeconom.2005.01.008
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00459667
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    More about this item

    Keywords

    Multivariate MSM; Maximum likelihood; Particle filter; Markov-switching; Stochastic volatility; Multifrequency volatility decomposition; Value-at-risk; Quantile forecasts;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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

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