文档介绍：Multifractal Spectral Analysis of the 1987 Stock
Market Crash
Cornelis A. Los* and Rossitsa Yalamova**
*Kent State University, Department of Finance, BSA416,
Kent, OH, 44242-0001, Email: clos500@
**University of Lethbridge, Faculty of Management,
Finance, E520 University Hall, Canada T1K 3M4
Email: rossitsa.******@
July 20, 2004
Abstract
The multifractal model of asset returns captures the volatility persis-
tence of many financial time series. Its multifractal puted
from wavelet modulus maxima lines provides the spectrum of irregular-
ities in the distribution of market returns over time and thereby of the
kind of uncertainty or "randomness" in a particular market. Changes in
this multifractal spectrum display distinctive patterns around substantial
market crashes or “drawdowns." In other words, the kinds of singularities
and the kinds of irregularity change in a distinct fashion in the periods
immediately preceding and following major market drawdowns. This pa-
per focuses on these identifiable multifractal spectral patterns surround-
ing the stock market crash of 1987. Although we are not able to find
auniquelyidentifiable irregularity pattern within the same market pre-
ceding different crashes at different times, we do find the same uniquely
identifiable pattern in various stock markets experiencing the same crash
at the same time. Moreover, our results suggest that all such crashes are
preceded by a gradual increase in the weighted average of the values of
the Lipschitz regularity exponents, under low dispersion of the multifrac-
tal spectrum. At a crash, this weighted average irregularity value drops
to a much lower value, while the dispersion of the spectrum of Lipschitz
exponents jumps up to a much higher level after the crash. Our most
striking result, however, is that the multifractal spectra of stock market
returns are not stationary. Also, while the stock market returns show a
global Hurs