Research Discussion Papers, Bank of Finland
No 27/2005:
A wavelet analysis of scaling laws and long-memory in stock market volatility
Tommi Vuorenmaa ()
Abstract: This paper investigates the dependence of average stock
market volatility on the timescale or on the time interval used to measure
price changes, which dependence is often referred to as the scaling law.
Scaling factor, on the other hand, refers to the elasticity of the
volatility measure with respect to the timescale. This paper studies, in
particular, whether the scaling factor differs from the one in a simple
random walk model and whether it has remained stable over time. It also
explores possible underlying reasons for the observed behaviour of
volatility in terms of heterogeneity of stock market players and
periodicity of in-traday volatility. The data consist of volatility series
of Nokia Oyj at the Helsinki Stock Exchange at five minute frequency over
the period from January 4, 1999 to December 30, 2002. The paper uses
wavelet methods to decompose stock market volatility at different
timescales. Wavelet methods are particularly well motivated in the present
context due to their superior ability to describe local properties of times
se-ries. The results are, in general, consistent with multiscaling in
Finnish stock markets. Furthermore, the scaling factor and the long-memory
parameters of the volatility series are not constant over time, nor
con-sistent with a random walk model. Interestingly, the evidence also
suggests that, for a significant part, the behaviour of volatility is
accounted for by an intraday volatility cycle referred to as the New York
effect. Long-memory features emerge more clearly in the data over the
period around the burst of the IT bubble and may, consequently, be an
indication of irrational exuberance on the part of investors.
Keywords: long-memory; scaling; stock market; volatility; wavelets; (follow links to similar papers)
JEL-Codes: C14; C22; (follow links to similar papers)
44 pages, October 11, 2005
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