Volatility Comovement: A Multifrequency Approach
41 Pages Posted: 31 Aug 2004
Date Written: April 2004
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.
Keywords: Multivariate MSM, comovement, maximum likelihood, particle filter, Markov-switching, stochastic volatility, multifrequency volatility decomposition, value at risk, quantile forecasts
JEL Classification: C13, C32, F37, G15
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