Extreme value theory for stochastic integrals of Legendre polynomials
AbstractWe study in this paper the extremal behavior of stochastic integrals of Legendre polynomial transforms with respect to Brownian motion. As the main results, we obtain the exact tail behavior of the supremum of these integrals taken over intervals [0,h] with h>0 fixed, and the limiting distribution of the supremum on intervals [0,T] as T-->[infinity]. We show further how this limit distribution is connected to the asymptotic of the maximally selected quasi-likelihood procedure that is used to detect changes at an unknown time in polynomial regression models. In an application to global near-surface temperatures, we demonstrate that the limit results presented in this paper perform well for real data sets.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 100 (2009)
Issue (Month): 5 (May)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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"Tests for Parameter Instability and Structural Change with Unknown Change Point,"
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- Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
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- Aue, Alexander & Horváth, Lajos & Hušková, Marie, 2012. "Segmenting mean-nonstationary time series via trending regressions," Journal of Econometrics, Elsevier, vol. 168(2), pages 367-381.
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