Multivariate COGARCH(1,1) processes

Multivariate $\operatorname {COGARCH}(1,1)$ processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate L\'{e}vy process and the latent time-varying covariance matrix is directly specified as a stochastic process in the positive semidefinite matrices. After defining the $\operatorname {COGARCH}(1,1)$ process, we analyze its probabilistic properties. We show a sufficient condition for the existence of a stationary distribution for the stochastic covariance matrix process and present criteria ensuring the finiteness of moments. Under certain natural assumptions on the moments of the driving L\'{e}vy process, explicit expressions for the first and second-order moments and (asymptotic) second-order stationarity of the covariance matrix process are obtained. Furthermore, we study the stationarity and second-order structure of the increments of the multivariate $\operatorname {COGARCH}(1,1)$ process and their "squares".Comment: Published in at http://dx.doi.org/10.3150/09-BEJ196 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

First Run II Measurement of the W Boson Mass with CDF

The CDF collaboration has analyzed ~200/pb of Tevatron Run II data taken between February 2002 and September 2003 to measure the W boson mass. With a sample of 63964 W->e nu decays and 51128 W->mu nu decays, we measure M_W = 80413+-34(stat)+-34(syst) MeV. The total measurement uncertainty of 48 MeV makes this result the most precise single measurement of the W boson mass to date.Comment: Conference Proceedings for Rencontres de Moriond EW 200