Testing composite hypotheses for locally stationary processes

Kenji Sakiyama*, Masanobu Taniguchi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


For a class of locally stationary processes introduced by Dahlhaus, this paper discusses the problem of testing composite hypotheses. First, for the Gaussian likelihood ratio test (GLR), Wald test (W) and Lagrange multiplier test (LM), we derive the limiting distribution under a composite hypothesis in parametric form. It is shown that the distribution of GLR, W and LM tends to χ2 distribution under the hypothesis. We also evaluate their local powers under a sequence of local alternatives, and discuss their asymptotic optimality. The results can be applied to testing for stationarity. Some examples are given. They illuminate the local power property via simulation. On the other hand, we provide a nonparametric LAN theorem. Based on this result, we obtain the limiting distribution of the GLR under both null and alternative hypotheses described in nonparametric form. Finally, the numerical studies are given.

Original languageEnglish
Pages (from-to)483-504
Number of pages22
JournalJournal of Time Series Analysis
Issue number4
Publication statusPublished - 2003 Jul
Externally publishedYes


  • Gaussian likelihood ratio test
  • Lagrange multiplier test
  • Local asymptotic normality
  • Local power
  • Locally asymptotically optimal test
  • Locally stationary processes
  • Tests for stationarity
  • Time-varying spectral density
  • Transfer function
  • Wald test

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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