Empirical Likelihood and Quantile Methods for Time Series

1. Front Matter

   Pages i-x

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2. Introduction

   • Yan Liu, Fumiya Akashi, Masanobu Taniguchi

   Pages 1-27

3. Parameter Estimation Based on Prediction

   • Yan Liu, Fumiya Akashi, Masanobu Taniguchi

   Pages 29-57

4. Quantile Method for Time Series

   • Yan Liu, Fumiya Akashi, Masanobu Taniguchi

   Pages 59-86

5. Empirical Likelihood Method for Time Series

   • Yan Liu, Fumiya Akashi, Masanobu Taniguchi

   Pages 87-108

6. Self-weighted GEL Methods for Infinite Variance Processes

   • Yan Liu, Fumiya Akashi, Masanobu Taniguchi

   Pages 109-130

7. Back Matter

   Pages 131-136

   PDF

This book integrates the fundamentals of asymptotic theory of statistical inference for time series under nonstandard settings, e.g., infinite variance processes, not only from the point of view of efficiency but also from that of robustness and optimality by minimizing prediction error. This is the first book to consider the generalized empirical likelihood applied to time series models in frequency domain and also the estimation motivated by minimizing quantile prediction error without assumption of true model. It provides the reader with a new horizon for understanding the prediction problem that occurs in time series modeling and a contemporary approach of hypothesis testing by the generalized empirical likelihood method. Nonparametric aspects of the methods proposed in this book also satisfactorily address economic and financial problems without imposing redundantly strong restrictions on the model, which has been true until now. Dealing with infinite variance processes makesanalysis of economic and financial data more accurate under the existing results from the demonstrative research. The scope of applications, however, is expected to apply to much broader academic fields. The methods are also sufficiently flexible in that they represent an advanced and unified development of prediction form including multiple-point extrapolation, interpolation, and other incomplete past forecastings. Consequently, they lead readers to a good combination of efficient and robust estimate and test, and discriminate pivotal quantities contained in realistic time series models.

• Empirical Likelihood
• Quantile Score
• Heavy Tail
• Efficiency
• Robustness

“The book is devoted to some questions of statistical inference for time series models. … The book can be useful for researches who are interested in time series analysis and statistical inference.” (Jonas Šiaulys, zbMath 1418.62012, 2019)

• Kyoto University/RIKEN AIP, Kyoto, Japan

  Yan Liu

• Waseda University, Tokyo, Japan

  Fumiya Akashi, Masanobu Taniguchi

Yan Liu, Dr., Waseda University, y.liu2@kurenai.waseda.jp, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan


Fumiya Akashi, Dr., Waseda University, f.akashi@kurenai.waseda.jp, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan


Masanobu Taniguchi, Professor, Research Importance Position, Research Institute for Science & Engineering, Waseda University, taniguchi@waseda.jp, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

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