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A wavelet analysis of scaling laws and long-memory in stock market volatility

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  • Vuorenmaa, Tommi A.

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.

Suggested Citation

  • Vuorenmaa, Tommi A., 2005. "A wavelet analysis of scaling laws and long-memory in stock market volatility," Bank of Finland Research Discussion Papers 27/2005, Bank of Finland.
  • Handle: RePEc:zbw:bofrdp:rdp2005_027
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    References listed on IDEAS

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    1. Andersen, Torben G & Bollerslev, Tim, 1997. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    2. Torben G. Andersen & Tim Bollerslev, 1997. "Answering the Critics: Yes, ARCH Models Do Provide Good Volatility Forecasts," NBER Working Papers 6023, National Bureau of Economic Research, Inc.
    3. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    4. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    5. Bollerslev, Tim & Wright, Jonathan H., 2000. "Semiparametric estimation of long-memory volatility dependencies: The role of high-frequency data," Journal of Econometrics, Elsevier, vol. 98(1), pages 81-106, September.
    6. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
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    More about this item

    Keywords

    long-memory; scaling; stock market; volatility; wavelets;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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