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Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash

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Author Info

  • CORNELIS A. LOS

    (Kent State University)

  • ROSSITSA M. YALAMOVA

    (University of Lethbridge)

Abstract

The multifractal model of asset returns captures the volatility persistence of many financial time series. Its multifractal spectrum computed from wavelet modulus maxima lines provides the spectrum of irregularities 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 paper focuses on these identifiable multifractal spectral patterns surrounding the stock market crash of 1987. Although we are not able to find a uniquely identifiable irregularity pattern within the same market preceding 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 multifractal 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, therefore, is that the multifractal spectra of stock market returns are not stationary. Also, while the stock market returns show a global Hurst exponent of slight persistence 0.5

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File URL: http://128.118.178.162/eps/fin/papers/0409/0409050.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0409050.

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Date of creation: 18 Sep 2004
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Handle: RePEc:wpa:wuwpfi:0409050

Note: Type of Document - pdf. Los, Cornelis A. and Yalamova, Rossitsa M., 'Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash' (July 2004).
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Web page: http://128.118.178.162

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Keywords: Financial Markets; Persistence; Multi-Fractal Spectral Analysis; Wavelets;

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  1. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
  2. David Hirshleifer & Siew Hong Teoh, 2003. "Herd Behaviour and Cascading in Capital Markets: a Review and Synthesis," European Financial Management, European Financial Management Association, vol. 9(1), pages 25-66.
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  7. Robert J. Elliott & John van der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330.
  8. Jean-Pierre Zigrand & Jon Danielsson, 2001. "What happens when you regulate risk?: evidence from a simple equilibrium model," LSE Research Online Documents on Economics 25069, London School of Economics and Political Science, LSE Library.
  9. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
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Cited by:
  1. Delavari, Majid & Gandali Alikhani, Nadiya, 2012. "The Effect of Crude Oil Price on the Methanol price," MPRA Paper 49727, University Library of Munich, Germany.

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