A Wavelet Analysis of Scaling Laws and Long-Memory in Stock Market Volatility

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 intraday 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 series. 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 consistent 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.