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Extreme value theory for stochastic integrals of Legendre polynomials

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  • Aue, Alexander
  • Horvth, Lajos
  • Huskov, Marie

Abstract

We 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.

Suggested Citation

  • Aue, Alexander & Horvth, Lajos & Huskov, Marie, 2009. "Extreme value theory for stochastic integrals of Legendre polynomials," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1029-1043, May.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:1029-1043
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    References listed on IDEAS

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    1. Albin, J. M. P., 1992. "On the general law of iterated logarithm with application to selfsimilar processes and to Gaussian processes in n and Hilbert space," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 1-31, May.
    2. Jandhyala, V. K. & MacNeill, I. B., 1989. "Residual partial sum limit process for regression models with applications to detecting parameter changes at unknown times," Stochastic Processes and their Applications, Elsevier, vol. 33(2), pages 309-323, December.
    3. 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.
    4. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    5. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    6. Albin, J. M. P., 2001. "On extremes and streams of upcrossings," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 271-300, August.
    7. V. K. Jandhyala & I. B. MacNeill, 1997. "Iterated Partial Sum Sequences of Regression Residuals and Tests for Changepoints with Continuity Constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 147-156.
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    Cited by:

    1. Krzysztof Dȩbicki & Enkelejd Hashorva & Lanpeng Ji & Chengxiu Ling, 2015. "Extremes of order statistics of stationary processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 229-248, June.
    2. 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.
    3. Lajos Horváth & William Pouliot & Shixuan Wang, 2017. "Detecting at-Most-m Changes in Linear Regression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 552-590, July.

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