TY  - JOUR
AU  - Calvet,Laurent E.
AU  - Fisher,Adlai J.
AU  - Thompson,Samuel B.
TI  - Volatility Comovement: A Multifrequency Approach
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 300
PY  - 2004
Y2  - August 2004
UR  - http://www.nber.org/papers/t0300
L1  - http://www.nber.org/papers/t0300.pdf
N1  - Author contact info:
Laurent E. Calvet
Department of Finance
HEC Paris
1 rue de la Libération
78351 Jouy en Josas
France
Tel: +33 13 967 9409
Fax: +33 13 967 7085
E-Mail: calvet@hec.fr

Adlai Fisher
Sauder School of Business
University of British Columbia
2053 Main Mall, Vancouver BC, CANADA
V6T 1Z2
Tel: 604 822 8331
Fax: 604 822 4695
E-Mail: adlai.fisher@sauder.ubc.ca

Samuel Thompson
Arrowstreet Capital, L.P. 
E-Mail: sambthompson@gmail.com
AB  - 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.
ER  -