Wilmott - Long Memory And Regime Shifts In Asset Volatility.pdf

文档介绍：Long Memory and
Regime Shifts in
Asset Volatility
Jonathan Kinlay,
Partner, Investment Analytics, ******@investment-
Volatility Autocorrelations
Long Memory
The conditional distribution of asset volatility has been the sub-
ject of extensive empirical research in the last decade. The over-
whelming preponderance of evidence points to the existence of DJIA
pronounced long term dependence in volatility, characterized by BA
slow decay rates in autocorrelations and significant correlations at DD

long lags (. Crato and de Lima, 1993, and Ding, Granger and GE
Engle, 1993). Andersen, et al, 1999, find similar patterns for auto- HWP
correlations in the realized volatility processes for the Dow 30 IBM
stocks—autocorrelations remain systematically above the conven-
tional Bartlett 95% confidence band as far out as 120 days. 1 4 7 1013161922
Comparable results are seen when autocorrelations are examined −
for daily log range volatility, as the figure below illustrates. Here Months
we see significant autocorrelations in some stocks as far back as
two years.
hydrologist Harold Hurst (1951). The classical rescaled range statistic is
Long Memory Detection and Estimation defined as
Among the first to consider the possibility of persistent statistical k k 
¯ ¯
dependence in financial time series was Mandelbr