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Exponential tilted likelihood for stationary time series models

Xiuzhen Zhang ,

Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE, School of Statistics, East China Normal University, Shanghai, People’s Republic of China; School of Mathematics and Statistics, Shanxi Datong University, Datong, People’s Republic of China

Yukun Liu ,

Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE, School of Statistics, East China Normal University, Shanghai, People’s Republic of China

Riquan Zhang ,

Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE, School of Statistics, East China Normal University, Shanghai, People’s Republic of China

Zhiping Lu

Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE, School of Statistics, East China Normal University, Shanghai, People’s Republic of China

Pages 0 | Received 21 Mar. 2021, Accepted 02 Sep. 2021, Published online: 23 Sep. 2021,
  • Abstract
  • Full Article
  • References
  • Citations

Depending on the asymptotical independence of periodograms, exponential tilted (ET) likelihood, as an effective nonparametric statistical method, is developed to deal with time seriesin this paper. Similar to empirical likelihood (EL), it still suffers from two drawbacks: the nondefinition problem of the likelihood function and the under-coverage probability of confidenceregion. To overcome these two problems, we further proposed the adjusted ET (AET) likelihood.With a specific adjustment level, our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method. In addition, due to the good performance of ET under moment model misspecification [Schennach, S. M. (2007). Point estimation with exponentially tilted empirical likelihood. The Annals of Statistics, 35(2), 634–672.https://doi.org/10.1214/009053606000001208], we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1). The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation. A real data set is analyzed for illustration purpose

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To cite this article: Xiuzhen Zhang, Yukun Liu, Riquan Zhang & Zhiping Lu (2021): Exponential
tilted likelihood for stationary time series models, Statistical Theory and Related Fields, DOI:
10.1080/24754269.2021.1978207
To link to this article: https://doi.org/10.1080/24754269.2021.1978207

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