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


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  • Ching-Kang Ing

    (Institute of Statistical Science, Academia Sinica)

  • Ching-Zong Wei

    (Institute of Statistical Science, Academia Sinica)

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    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.

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    Bibliographic Info

    Paper provided by EconWPA in its series Econometrics with number 0508009.

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    Length: 22 pages
    Date of creation: 07 Aug 2005
    Date of revision:
    Handle: RePEc:wpa:wuwpem:0508009

    Note: Type of Document - pdf; pages: 22
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    Keywords: Autoregressive fractionally integrated moving average; long range dependence; maximal inequality; model selection; convergence system; strong consistency.;

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    1. 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.
    2. 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.
    3. Kokoszka, Piotr & Leipus, Remigijus, 1998. "Change-point in the mean of dependent observations," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 385-393, November.
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