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Measurement of Financial Risk Persistence

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  • Cornelis A. Los

    (Kent State University)

Abstract

This paper discusses various ways of measuring the persistence or Long Memory (LM) of financial market risk in both its time and frequency domains. For the measurement of the risk, irregularity or 'randomness' of these series, we can compute a set of critical Lipschitz - Hölder exponents, in particular, the Hurst Exponent and the Lévy Stability Alpha, and relate them to the Mandelbrot-Hoskings' fractional difference operators, as occur in the Fractional Brownian Motion model (which is our benchmark). The main contribution of this paper is to provide a compaison table of the various critical exponents available in various scientific disciplines to measure the LM persistence of time seies. It also discusses why Markov- and (G)ARCH models cannot capture this LM, long term dependence or risk persistence, because these models have finite lag lengths, while the empirically observed long memory risk phenomenon is an infinite lag length phenomenon. Currently, there are three techniques of nonstationary time series analysis to measure time - varying financial risk: Range/Scale analysis, windowed Fourier analysis, and wavelet MRA. This paper relates these powerful analytic techniques to classical Box-Jenkins-type time series analysis and to Pearson's spectral frequency analysis, which both rely on the uncorroboated assumption of stationarity and ergodicity.

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File URL: http://128.118.178.162/eps/fin/papers/0502/0502013.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0502013.

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Length: 37 pages
Date of creation: 13 Feb 2005
Date of revision:
Handle: RePEc:wpa:wuwpfi:0502013

Note: Type of Document - pdf; pages: 37
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Web page: http://128.118.178.162

Related research

Keywords: Persistence; long memory; dependence; time series; frequency; critical exponents; fractional Brownian motion; (G)ARCH; risk measurement;

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References

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  1. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Baillie, R.T. & Bollerslev, R.T., 1990. "Prediction In Dynamic Models With Time Dependent Conditional Variances," Papers 8815, Michigan State - Econometrics and Economic Theory.
  4. Akgiray, Vedat, 1989. "Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts," The Journal of Business, University of Chicago Press, vol. 62(1), pages 55-80, January.
  5. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  6. Andrew W. Lo & A. Craig MacKinlay, 1987. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc.
  7. Sutthisit Jamdee & Cornelis A. Los, 2004. "Long Memory Options: Valuation," Finance 0409049, EconWPA.
  8. Cornelis A. Los, 2004. "Nonparametric Efficiency Testing of Asian Stock Markets Using Weekly Data," Finance 0409033, EconWPA.
  9. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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Cited by:
  1. Cornelis A. Los, 2005. "The Degree of Stability of Price Diffusion," Finance 0508006, EconWPA.

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