2004/11/30 by Zhengjun Zhang, Richard L. Smith · 3 citations
Economics, Econometrics and Finance · Decision Sciences · #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Forecasting Techniques and Applications
paper · doi:10.1239/jap/1101840556
In the characterization of multivariate extremal indices of multivariate stationary processes, multivariate maxima of moving maxima processes, or M4 processes for short, have been introduced by Smith and Weissman. Central to the introduction of M4 processes is that the extreme observations of multivariate stationary processes may be characterized in terms of a limiting max-stable process under quite general conditions, and that a max-stable process can be arbitrarily closely approximated by an M4 process. In this paper, we derive some additional basic probabilistic properties for a finite class of M4 processes, each of which contains finite-range clustered moving patterns, called signature patterns, when extreme events occur. We use these properties to construct statistical estimation schemes for model parameters.