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Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash

Author

Listed:
  • 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

Suggested Citation

  • Cornelis A. Los & Rossitsa M. Yalamova, 2004. "Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash," Finance 0409050, University Library of Munich, Germany.
    • 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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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0409/0409050.pdf
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    References listed on IDEAS

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    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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    More about this item

    Keywords

    Financial Markets; Persistence; Multi-Fractal Spectral Analysis; Wavelets;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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