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Author
Małecka Marta (University of Lodz, Poland), Pekasiewicz Dorota (University of Lodz, Poland)
Title
A Modification of the Probability Weighted Method of Moments and its Application to Estimate The Financial Return Distribution Tail
Source
Statistics in Transition, 2013, vol. 14, nr 3, s. 495-506, rys., tab., bibliogr. 9 poz.
Keyword
Rozkład Pareta, Prawdopodobieństwo, Estymacja, Finanse
Pareto distribution, Probability, Estimation, Finance
Note
Materiały z konferencji Multivariate Statistical Analysis 2013, Łódź.
summ.
Abstract
The issue of fitting the tail of the random variable with an unknown distribution plays a pivotal role in finance statistics since it paves the ground for estimation of high quantiles and subsequently offers risk measures. The parametric estimation of fat tails is based on the convergence to the generalized Pareto distribution (GPD). The paper explored the probability weighted method of moments (PWMM) applied to estimation of the GPD parameters. The focus of the study was on the tail index, commonly used to characterize the degree of tail fatness. The PWMM algorithm requires specification of the cdf estimate of the so-called excess variable and depends on the choice of the order of the probability weighted moments. We suggested modification of the PWMM method through the application of the level crossing empirical distribution function. Through the simulation study, the paper investigated statistical properties of the GPD shape parameter estimates with reference to the PWMM algorithm specification. The simulation experiment was designed with the use of fat-tailed distributions with parameters assessed on the basis of the empirical daily data for DJIA index. The results showed that, in comparison to the commonly used cdf formula, the choice of the level crossing empirical distribution function improved the statistical properties of the PWMM estimates. As a complementary analysis, the PWMM tail estimate of DJIA log returns distribution was presented. (original abstract)
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Bibliography
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ISSN
1234-7655
Language
eng
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