On Tail Index Estimation for Dependent, Heterogeneous Data
نویسنده
چکیده
In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by Hill (1975) for dependent, heterogeneous processes. We develop new extremal dependence measures that characterize a massive array of linear, nonlinear, and conditional volatility processes with long or short memory. We prove that the Hill estimator is weakly and uniformly weakly consistent for processes with extremes that form mixingale sequences and asymptotically normal for processes with extremes that are near epoch dependent (NED) on some arbitrary mixing functional. The extremal persistence assumptions in this paper are known to hold for mixing, L p-NED, and some non-L p-NED processes, including ARFIMA, FIGARCH, explosive GARCH, nonlinear ARMA-GARCH, and bilinear processes, and nonlinear distributed lags like random coefficient and regime-switching autoregressions. Finally, we deliver a simple nonparametric estimator of the asymptotic variance of the Hill estimator and prove consistency for processes with NED extremes.
منابع مشابه
On functional central limit theorems for dependent, heterogeneous arrays with applications to tail index and tail dependence estimation
Article history: Received 18 September 2007 Received in revised form 27 June 2008 Accepted 21 September 2008 Available online 2 October 2008
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