DYNAMIC MODELS FOR VOLATILITY AND HEAVY TAILS: WITH APPLICATIONS TO FINANCIAL AND ECONOMIC TIME SERIES, BY A. C. HARVEY. PUBLISHED BY CAMBRIDGE UNIVERSITY PRESS, 2013 NEW YORK, USA. TOTAL NUMBER OF PAGES: 261. PRICE: $36.99. ISBN: 978-1-107-63002-4

摘要

The time-series properties of many financial, and some economic, variables are characterized by time-varying volatility and outliers. Following the seminal contribution of Engle (1982), a popular method for capturing time-varying volatility is the use of autoregressive conditional heteroscedasticity (ARCH) models - or their extension, generalized ARCH (GARCH) models (Bollerslev, 1986) - in which the conditional variance is an autoregressive process of either finite or implicitly infinite order. In their simplest form, this approach models the variable of interest as the product of the square root of the conditional variance and a Gaussian white noise innovation (with unit variance). While such models imply fatter tails than the normal, maximum likelihood estimates based on this assumed structure have been found to be sensitive to outliers. This sensitivity can be reduced by replacing the Gaussian with a Student-t distribution; see Bollerslev (1987). However, the nature of the recursions implicit in GARCH models mean that outliers can affect the conditional variance some distance into the future, a feature that can be argued to contradict the concept of an 'outlier'. Additionally, once Gaussianity is dropped, it may not be the case that volatility is best captured via the variance, suggesting a need to look beyond GARCH models for time series with heavy-tailed distributions.