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Measurement of Financial Risk Persistence

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Author Info
Cornelis A. Los (Kent State University)

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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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Publisher 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
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Handle: RePEc:wpa:wuwpfi:0502013

Note: Type of Document - pdf; pages: 37
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Web page: http://129.3.20.41

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

Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Cornelis A. Los, 2004. "Nonparametric Efficiency Testing of Asian Stock Markets Using Weekly Data," Finance 0409033, EconWPA. [Downloadable!]
  2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(1), pages 41-66. [Downloadable!] (restricted)
    Other versions:
  6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  7. Sutthisit Jamdee & Cornelis A. Los, 2004. "Long Memory Options: Valuation," Finance 0409049, EconWPA. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Cornelis A. Los, 2005. "The Degree of Stability of Price Diffusion," Finance 0508006, EconWPA. [Downloadable!]
Statistics
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