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A maximal moment inequality for long range dependent time series with applications to estimation and model selection

Author

Listed:
  • Ching-Kang Ing

    (Institute of Statistical Science, Academia Sinica)

  • Ching-Zong Wei

    (Institute of Statistical Science, Academia Sinica)

Abstract

We establish a maximal moment inequality for the weighted sum of a long- range dependent process. An extension to H$\acute{a}$jek-R$\acute{e}$ny and Chow's type inequality is then obtained. It enables us to deduce a strong law for the weighted sum of a stationary long-range dependent time series. To illustrate its usefulness, applications of the inequality to estimation and model selection in multiple regression models with long-range dependent errors are given.

Suggested Citation

  • Ching-Kang Ing & Ching-Zong Wei, 2005. "A maximal moment inequality for long range dependent time series with applications to estimation and model selection," Econometrics 0508009, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0508009
    Note: Type of Document - pdf; pages: 22
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    References listed on IDEAS

    as
    1. Chen, Zhao-Guo & Ni, Jun-Yuan, 1989. "Subset regression time series and its modeling procedures," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 266-288, November.
    2. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    3. Marc Lavielle & Eric Moulines, 2000. "Least‐squares Estimation of an Unknown Number of Shifts in a Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 33-59, January.
    4. Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
    5. Kokoszka, Piotr & Leipus, Remigijus, 1998. "Change-point in the mean of dependent observations," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 385-393, November.
    6. Gui-Jing, Chen & Lai, T. L. & Wei, C. Z., 1981. "Convergence systems and strong consistency of least squares estimates in regression models," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 319-333, September.
    7. Lai, T. L. & Wei, C. Z., 1982. "Asymptotic properties of projections with applications to stochastic regression problems," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 346-370, September.
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    More about this item

    Keywords

    Autoregressive fractionally integrated moving average; long range dependence; maximal inequality; model selection; convergence system; strong consistency.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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