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Wavelet change‐point estimation for long memory non‐parametric random design models

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  • Lihong Wang
  • Haiyan Cai

Abstract

For a random design regression model with long memory design and long memory errors, we consider the problem of detecting a change point for sharp cusp or jump discontinuity in the regression function. Using the wavelet methods, we obtain estimators for the change point, the jump size and the regression function. The strong consistencies of these estimators are given in terms of convergence rates.

Suggested Citation

  • Lihong Wang & Haiyan Cai, 2010. "Wavelet change‐point estimation for long memory non‐parametric random design models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 86-97, March.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:2:p:86-97
    DOI: 10.1111/j.1467-9892.2009.00646.x
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    1. Javier Hidalgo & Peter M Robinson, 1997. "Time Series Regression with Long Range Dependence - (Now published in 'Annals of Statistics', 25, (1997)pp.2054-2083.)," STICERD - Econometrics Paper Series 318, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Cheng, Bing & Robinson, P. M., 1994. "Semiparametric estimation from time series with long-range dependence," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 335-353.
    3. Véronique Delouille & Rainer Sachs, 2005. "Estimation of nonlinear autoregressive models using design-adapted wavelets," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 235-253, June.
    4. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
    5. V. Delouille & J. Simoens & R. von Sachs, 2004. "Smooth Design-Adapted Wavelets for Nonparametric Stochastic Regression," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 643-658, January.
    6. Javier Hidalgo, 1997. "Non‐Parametric Estimation With Strongly Dependent Multivariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(2), pages 95-122, March.
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    Cited by:

    1. Zhou, Xing-cai & Lin, Jin-guan, 2013. "Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 251-270.

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