Estimating the Density Tail Index for Financial Time Series

Phillip Kearns · Adrian Pagan

135 citations0/0 files storedThe Review of Economics and Statistics

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Probability and Risk Models Financial Risk and Volatility Modeling Complex Systems and Time Series Analysis

Abstract

The tail index of a density has been widely used as an indicator of the probability of getting a large deviation in a random variable. Most of the theory underlying popular estimators of it assume that the data are independently and identically distributed (i.i.d.). However, many recent applications of the estimator have been to financial data, and such data tend to exhibit long-range dependence. We show, via Monte Carlo simulations, that conventional measures of the precision of the estimator, which are based on the i.i.d. assumption, are greatly exaggerated when such dependent data are used. This conclusion also has implications for estimates of the likelihood of getting some extreme values, and we illustrate the changed conclusions one would get using equity return data.

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References

1965The Behavior of Stock-Market Prices 1963The Variation of Certain Speculative Prices 1997The variation of certain speculative prices 1992ARCH modeling in finance 1974A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices 1994Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets 1989On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective 1990Indexes of U.S. Stock Prices from 1802 to 1987

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2005Empirical distributions of stock returns: between the stretched exponential and the power law?2001Margin exceedences for European stock index futures using extreme value theory 2010ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATA 2016Tail Risk Dynamics in Stock Returns: Links to the Macroeconomy and Global Markets Connectedness 2014Statistics of Heteroscedastic Extremes 2002

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