Generalised likelihood ratio tests for spectral density

Jianqing Fan, Wenyang Zhang

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


There are few techniques available for testing whether or not a family of parametric times series models fits a set of data reasonably well without serious restrictions on the forms of alternative models. In this paper, we consider generalised likelihood ratio tests of whether or not the spectral density function of a stationary time series admits certain parametric forms. We propose a bias correction method for the generalised likelihood ratio test of Fan et al. (2001). In particular, our methods can be applied to test whether or not a residual series is white noise. Sampling properties of the proposed tests are established. A bootstrap approach is proposed for estimating the null distribution of the test statistics. Simulation studies investigate the accuracy of the proposed bootstrap estimate and compare the power of the various ways of constructing the generalised likelihood ratio tests as well as some classic methods like the Cramér-von Mises and Ljung-Box tests. Our results favour the newly proposed bias reduction method using the local likelihood estimator.

Original languageEnglish (US)
Pages (from-to)195-209
Number of pages15
Issue number1
StatePublished - 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • ARMA model
  • Generalised likelihood ratio test
  • Local least squares
  • Local likelihood
  • Periodogram
  • Spectral density


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