Volatility Comovement: A Multifrequency Approach
NBER Technical Working Paper No. 300
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.
Published: Calvet, Laurent E., Adlai J. Fisher and Samuel B. Thompson. "Volatility Comovement: A Multifrequency Approach," Journal of Econometrics, 2006, v131(1-2,Mar-Apr), 179-215.