Latent model extreme value index estimation

Abstract

We propose a novel strategy for multivariate extreme value index estimation. In applications such as finance, volatility and risk of multivariate time series are often driven by the same underlying factors. To estimate the latent risks, we apply a two-stage procedure. First, a set of independent latent series is estimated using a method of latent variable analysis. Then, univariate risk measures are estimated individually for the latent series. We provide conditions under which the effect of the latent model estimation to the asymptotic behavior of the risk estimators is negligible. Simulations illustrate the theory under both i.i.d. and dependent data, and an application into currency exchange rate data shows that the method is able to discover extreme behavior not found by component-wise analysis of the original series.