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Rank Tests for Randomness Against Time-Varying MA Alternative

In: Research Papers in Statistical Inference for Time Series and Related Models

Author

Listed:
  • Junichi Hirukawa

    (Niigata University, Faculty of Science)

  • Shunsuke Sakai

    (Niigata University, Graduate School of Science and Technology)

Abstract

In this paper, we extend the idea of the problem of testing randomness against ARMA alternative to a class of locally stationary processes introduced by [1, 2]. We use the linear serial rank statistics and apply the notion of the contiguity [12] for the testing problem. Under the null hypothesis, the joint asymptotic normality of the proposed rank test statistics and log-likelihood ratio is established by making use of the local asymptotic normal property. Then, applying LeCam’s third lemma, the asymptotic normality of test statistic under the alternative is shown automatically.

Suggested Citation

  • Junichi Hirukawa & Shunsuke Sakai, 2023. "Rank Tests for Randomness Against Time-Varying MA Alternative," Springer Books, in: Yan Liu & Junichi Hirukawa & Yoshihide Kakizawa (ed.), Research Papers in Statistical Inference for Time Series and Related Models, chapter 0, pages 221-245, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-0803-5_9
    DOI: 10.1007/978-981-99-0803-5_9
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