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Local Whittle likelihood approach for generalized divergence

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  • Yujie Xue
  • Masanobu Taniguchi

Abstract

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.

Suggested Citation

  • Yujie Xue & Masanobu Taniguchi, 2020. "Local Whittle likelihood approach for generalized divergence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(1), pages 182-195, March.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:1:p:182-195
    DOI: 10.1111/sjos.12418
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