Asymptotic behavior of hill's estimator for autoregressive data

Sidney I. Resnick · Cătălin Stărică

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Probability and Risk Models Probability and Statistical Research Statistical Methods and Inference

Abstract

Consider a stationary, pth order autoregression satisfying whose innovation sequence is iid with regularly varying tail probabilities of index-α. From observations one may estimate by applying Hill's estimator to Alternatively, a second procedure is to use to get estimates of the autoregressive coefficients and then to estimate the residuals by and then to apply Hill's estimator to the estimated residuals. We show that from the point of asymptotic variance, the second procedure is superior

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References

1987Extreme Values, Regular Variation and Point Processes 1982On Some Simple Estimates of an Exponent of Regular Variation 1985Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities 1982Laws of Large Numbers for Sums of Extreme Values 1998Comparison of tail index estimators 1985On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation 1991On Tail Index Estimation Using Dependent Data 1997Smoothing the Hill Estimator

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