Measurement of Financial Risk Persistence

37 Pages Posted: 24 Feb 2005

See all articles by Cornelis A. Los

Cornelis A. Los

University of California at Irvine - The Paul Merage School of Business; EMEPS Associates

Multiple version iconThere are 2 versions of this paper

Date Written: February 13, 2005

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-Holder exponents, in particular, the Hurst Exponent and the Levy 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 series. 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.

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

JEL Classification: C15, C23, C53, G10

Suggested Citation

Los, Cornelis A., Measurement of Financial Risk Persistence (February 13, 2005). Available at SSRN: https://ssrn.com/abstract=666441 or http://dx.doi.org/10.2139/ssrn.666441

Cornelis A. Los (Contact Author)

University of California at Irvine - The Paul Merage School of Business ( email )

SB1
Irvine, CA 92697-3125
United States

HOME PAGE: http://merage.uci.edu/research-faculty/faculty-directory/Cornelis-Los.html

EMEPS Associates ( email )

Escondido, CA 92029
United States
760-294-0255 (Phone)
858-635-4783 (Fax)

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