Local Whittle likelihood approach for generalized divergence

Yujie Xue*, Masanobu Taniguchi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


There are many approaches in the estimation of spectral density. With regard to parametric approaches, different divergences are proposed in fitting a certain parametric family of spectral densities. Moreover, nonparametric approaches are also quite common considering the situation when we cannot specify the model of process. In this paper, we develop a local Whittle likelihood approach based on a general score function, with some special cases of which, the approach applies to more applications. This paper highlights the effective asymptotics of our general local Whittle estimator, and presents a comparison with other estimators. Additionally, for a special case, we construct the one-step ahead predictor based on the form of the score function. Subsequently, we show that it has a smaller prediction error than the classical exponentially weighted linear predictor. The provided numerical studies show some interesting features of our local Whittle estimator.

Original languageEnglish
Pages (from-to)182-195
Number of pages14
JournalScandinavian Journal of Statistics
Issue number1
Publication statusPublished - 2020 Mar 1


  • local Whittle likelihood
  • spectral density
  • stationary process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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