Regular Variation and Financial Time Series Models

Richard A. Davis
Colorado State University


In deriving the limit behavior of various central and extreme statistics,
such as the sample mean, the sample autocovariance and autocorrelation
functions, and sample maxima 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 financial
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

This is joint work with Thomas Mikosch and Bojan Basrak.