@techreport{NBERt0300,
 title = "Volatility Comovement: A Multifrequency Approach",
 author = "Laurent E. Calvet and Adlai J. Fisher and Samuel B. Thompson",
 institution = "National Bureau of Economic Research",
 type = "Working Paper",
 series = "Technical Working Paper Series",
 number = "300",
 year = "2004",
 month = "August",
 URL = "http://www.nber.org/papers/t0300",
 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.},
}