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A test for randomness against ARMA alternatives

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  • Dette, Holger
  • Spreckelsen, Ingrid

Abstract

In a recent paper, Mokkadem (1997. Stoch. Proc. Appl. 72, 145-149) derived a simple test for randomness against ARMA alternatives. In this note we consider a transformation of the corresponding statistic and present an alternative proof of this result. Through this approach it is demonstrated that the asymptotic distribution of the corresponding test statistic under the alternative does not depend on the fourth-order moments of the innovations. A simulation study indicates that a transformation of the test of Mokkadem (1997) (which is asymptotically equivalent to the classical portmanteau test) may perform better for finite sample sizes.

Suggested Citation

  • Dette, Holger & Spreckelsen, Ingrid, 2000. "A test for randomness against ARMA alternatives," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 131-139, September.
    • Handle: RePEc:eee:spapps:v:89:y:2000:i:1:p:131-139
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    References listed on IDEAS

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    1. Marc Hallin & Madan Lal Puri, 1994. "Aligned rank tests for linear models with autocorrelated errors," ULB Institutional Repository 2013/2045, ULB -- Universite Libre de Bruxelles.
    2. Hallin, M. & Puri, M. L., 1994. "Aligned Rank Tests for Linear Models with Autocorrelated Error Terms," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 175-237, August.
    3. Mokkadem, Abdelkader, 1997. "A measure of information and its applications to test for randomness against ARMA alternatives and to goodness-of-fit test," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 145-159, December.
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