Regular Variation and Financial Time Series Models

Talk 1 – Regular Variation and Financial Time Series Models

Abstract In deriving the limit behavior of various central and extreme statistics such as the sample mean, the sample autocovariance and autocorrelation functions, and sample maximia of strictly stationary processes with heavy-tails, multivariate regular variation and point process convergence theory play a central role. We first discuss an equivalence between multivariate regular variation of a random vector and regular variation of all finite linear combinations of the vector and its application to a result of Kesten concerning solutions of stochastic recursion equations In the second part of this talk, we show that a large class of time series models, including those arising from a stochastic recurrence equation such as GARCH, and stochastic volatility (SV) models, have finite dimensional distributions that are regularly varying. The implication of this property, as applied to the limit theory for the sample mean, autocovariance, and autocorrelation functions for these models, will be described. (This is joint work with Thomas Mikosch and Bojan Basrak.)