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On robust tail index estimation for linear long‐memory processes
Author(s) -
Beran Jan,
Das Bikramjit,
Schell Dieter
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2011.00774.x
Subject(s) - mathematics , statistic , index (typography) , test statistic , long memory , statistics , u statistic , estimation , statistical hypothesis testing , econometrics , efficiency , estimator , volatility (finance) , management , world wide web , computer science , economics
We consider robust estimation of the tail index α for linear long‐memory processes with i.i.d. innovations ε j following a symmetric α ‐stable law (1 < α < 2) and coefficients a j ∼ c · j − β . Estimates based on the left and right tail respectively are obtained together with a combined statistic with improved efficiency, and a test statistic comparing both tails. Asymptotic results are derived. Simulations illustrate the finite sample performance.