A Subsampling Approach to Estimating the Distribution of Diversing Statistics with Application to Assessing Financial Market Risks

In this paper we propose a subsampling estimator for the distribution of statistics diverging at either known or unknown rates when the underlying time series is strictly stationary and strong mixing. Based on our results we provide a detailed discussion how to estimate extreme order statistics with dependent data and present two applications to assessing financial market risk. Our method performs well in estimating Value at Risk and provides a superior alternative to Hill's estimator in operationalizing Safety First portfolio selection.

[1]  Joseph P. Romano,et al.  Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions , 1994 .

[2]  A. A. Weiss,et al.  Semiparametric estimates of the relation between weather and electricity sales , 1986 .

[3]  B. M. Hill,et al.  A Simple General Approach to Inference About the Tail of a Distribution , 1975 .

[4]  Charles M. Goldie,et al.  SLOW VARIATION WITH REMAINDER: THEORY AND APPLICATIONS , 1987 .

[5]  Clive W. J. Granger,et al.  Semiparametric estimates of the relation between weather and electricity sales , 1986 .

[6]  Vijay S. Bawa,et al.  Portfolio choice and equilibrium in capital markets with safety-first investors , 1977 .

[7]  Joseph P. Romano,et al.  On Subsampling Estimators with Unknown Rate of Convergence , 1999 .

[8]  J. Geluk,et al.  Regular variation, extensions and Tauberian theorems , 1987 .

[9]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[10]  Adrian Pagan,et al.  Estimating the Density Tail Index for Financial Time Series , 1997, Review of Economics and Statistics.

[11]  Peter Hall,et al.  Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems , 1990 .

[12]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[13]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[14]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .