Volatility comovement: a multifrequency approach

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.