Asymptotic behavior of hill's estimator for autoregressive data

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