On Tail Index Estimation for Dependent, Heterogenous Data
In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by B. Hill (1975) for possibly heavy- tailed, heterogenous, dependent processes. We prove the Hill estimator is weakly consistent for processes with extremes that form mixingale sequences, and asymptotically normal for processes with extremes that are near-epoch-dependent on the extremes of a mixing process. Our limit theory covers infinitely many ARFIMA and FIGARCH processes, stochastic recurrence equations, and simple bilinear processes. Moreover, we develop a simple non-parametric kernel estimator of the asymptotic variance of the Hill estimator, and prove consistency for extremal-NED processes.
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- Prasad V. Bidarkota & J. Huston McCulloch, .
"Optimal Univariate Inflation Forecasting with Symmetric Stable Shocks,"
Computing in Economics and Finance 1997
116, Society for Computational Economics.
- Prasad V. Bidarkota & J. Huston McCulloch, 1998. "Optimal univariate inflation forecasting with symmetric stable shocks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(6), pages 659-670.
- Davidson, James, 1993. "The Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes: The Asymptotically Degenerate Case," Econometric Theory, Cambridge University Press, vol. 9(03), pages 402-412, June.
- Akgiray, Vedat & Booth, G Geoffrey, 1988. "The Stable-Law Model of Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 51-57, January.
- repec:cup:etheor:v:13:y:1997:i:3:p:353-67 is not listed on IDEAS
- Chan, Ngai Hang & Tran, Lanh Tat, 1989. "On the First-Order Autoregressive Process with Infinite Variance," Econometric Theory, Cambridge University Press, vol. 5(03), pages 354-362, December.
- Caner, Mehmet, 1998. "Tests for cointegration with infinite variance errors," Journal of Econometrics, Elsevier, vol. 86(1), pages 155-175, June.
- Davidson, James, 1993. "An L1-convergence theorem for heterogeneous mixingale arrays with trending moments," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 301-304, March.
- Prasad Bidarkota & J Huston Mcculloch, 2004. "Testing for persistence in stock returns with GARCH-stable shocks," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 256-265.
- B. N. Cheng & S. T. Rachev, 1995. "Multivariate Stable Futures Prices," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 133-153.
- Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
- Davidson, James, 1992. "A Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes," Econometric Theory, Cambridge University Press, vol. 8(03), pages 313-329, September.
- de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(03), pages 353-367, June.
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