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Time series analysis via rank order theory: Signed-rank tests for ARMA models

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  • Hallin, Marc
  • Puri, Madan L.

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.

Suggested Citation

  • Hallin, Marc & Puri, Madan L., 1991. "Time series analysis via rank order theory: Signed-rank tests for ARMA models," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 1-29, October.
    • Handle: RePEc:eee:jmvana:v:39:y:1991:i:1:p:1-29
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    Cited by:

    1. Hallin, M. & Vermandele, C. & Werker, B.J.M., 2003. "Serial and Nonserial Sign-and-Rank Statistics : Asymptotic Representation and Asymptotic Normality," Discussion Paper 2003-23, Tilburg University, Center for Economic Research.
    2. 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.
    3. 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.
    4. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    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. 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.
    7. 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.
    8. 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.

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