Efficient Filtering of Financial Time Series and Extreme Value Theory

Posted: 27 Apr 2005

Abstract

We describe an efficient filtering process for a univariate time series, yt, for subsequent application of extreme value theory and the estimation of extreme quantiles, ie, value-at-risk. Our filtering model is based on a stationary ARMA-asymmetric Garch (1, 1) process. After filtering, the sequence of conditional residuals is approximately independent and identically distributed and therefore appropriate for the application of extreme value theory. The efficiency of the filtering process is of importance in this approach, and we apply an efficient estimator based on the generalized method of moments. The estimator is simple to compute but - more importantly - it is, in case of skewness or excess kurtosis of the conditional residuals, asymptotically efficient relative to the commonly applied quasi-maximum likelihood estimator. We further evaluate the robustness and efficiency of extreme value theory tail index estimators through a Monte Carlo study. An application to the daily returns of the ABB (Asea Brown Boveri) equity illustrates the methods, and a comparison is made with methods based on conditional normality, the conditional t-distribution and the empirical distribution function.

Keywords: Univariate time series, extreme value theory, EVT, value-at-risk, VAR, Monte Carlo, t-distribution

Suggested Citation

Nyström, Kaj and Skoglund, Jimmy, Efficient Filtering of Financial Time Series and Extreme Value Theory. Journal of Risk, Vol. 7, No. 2, pp. 63-84, Winter 2004/05, Available at SSRN: https://ssrn.com/abstract=707442

Kaj Nyström (Contact Author)

University of Umea ( email )

Samhallsvetarhuset, Plan 2
Umea University
Umeå, SE 901 87
Sweden

Jimmy Skoglund

SAS Institute Inc. ( email )

100 SAS Campus Drive
Cary, NC 27513-2414
United States

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