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Time series analysis via rank-order theory, signed-rank tests for ARMA models

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  • Marc Hallin
  • Madan Lal Puri

Abstract

An asymptotic distribution theory is developed for a general class of signed-rank serial statistics, and is then used to derive asymptotically locally optimal tests (in the maximin sense) for testing an ARMA model against other ARMA models. Special cases yield Fisher-Yates, van der Waerden, and Wilcoxon type tests. The asymptotic relative efficiencies of the proposed procedures with respect to each other, and with respect to their normal theory counterparts, are provided.
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Suggested Citation

  • Marc Hallin & Madan Lal Puri, 1991. "Time series analysis via rank-order theory, signed-rank tests for ARMA models," ULB Institutional Repository 2013/2029, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/2029
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    Cited by:

    1. Christian Genest, 2024. "A Conversation With Marc Hallin," International Statistical Review, International Statistical Institute, vol. 92(2), pages 137-159, August.
    2. Bernard Garel & Marc Hallin, 1995. "Local asymptotic normality of multivariate ARMA processes with a linear trend," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 551-579, September.
    3. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    4. Hallin, M. & Vermandele, C. & Werker, B.J.M., 2003. "Serial and Nonserial Sign-and-Rank Statistics : Asymptotic Representation and Asymptotic Normality," Other publications TiSEM 620d09ba-f476-426d-b236-3, Tilburg University, School of Economics and Management.
    5. Petar Sorić, 2020. "“Normal†growth of the Chinese economy: new metrics based on consumer confidence data," Economics Bulletin, AccessEcon, vol. 40(2), pages 1740-1746.
    6. Garel, Bernard & Hallin, Marc, 2000. "Rank-based partial autocorrelations are not asymptotically distribution-free," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 219-227, April.
    7. Mark van de Wiel, 2001. "The split-up algorithm: a fast symbolic method for computing p-values of distribution-free statistics," Computational Statistics, Springer, vol. 16(4), pages 519-538, December.
    8. J. Terpstra & M. Rao, 2001. "Generalized Rank Estimates For An Autoregressive Time Series: A U-Statistic Approach," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 155-179, May.
    9. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Karl B. Gregory & Soumendra N. Lahiri & Daniel J. Nordman, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 442-461, May.

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