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Volatility Comovement: A Multifrequency Approach

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  • Laurent E. Calvet
  • 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 (2001, 2004). Bivariate MSM is a stochastic volatility model with a closed-form likelihood. Estimation can proceed by ML 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. We extend the model to multivariate settings with a potentially large number of assets by proposing a parsimonious multifrequency factor structure.

Suggested Citation

  • Laurent E. Calvet & Adlai J. Fisher & Samuel B. Thompson, 2004. "Volatility Comovement: A Multifrequency Approach," NBER Technical Working Papers 0300, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0300
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    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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