Higher Order Asymptotic Theory for Time Series Analysis

1. Front Matter

   Pages I-VIII

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2. A Survey of the First-Order Asymptotic Theory for Time Series Analysis

   • Masanobu Taniguchi

   Pages 1-10

3. Higher Order Asymptotic Theory for Gaussian ARMA Processes

   • Masanobu Taniguchi

   Pages 11-61

4. Validity of Edgeworth Expansions in Time Series Analysis

   • Masanobu Taniguchi

   Pages 62-89

5. Higher Order Asymptotic Sufficiency, Asymptotic Ancillarity in Time Series Analysis

   • Masanobu Taniguchi

   Pages 90-103

6. Higher Order Investigations for Testing Theory in Time Series Analysis

   • Masanobu Taniguchi

   Pages 104-115

7. Higher Order Asymptotic Theory for Multivariate Time Series

   • Masanobu Taniguchi

   Pages 116-128

8. Some Practical Examples

   • Masanobu Taniguchi

   Pages 129-140

9. Back Matter

   Pages 141-162

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The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul­ tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.

• Covariance matrix
• Estimator
• Likelihood
• Time series
• Variance
• correlation

• Department of Mathematical Science, Faculty of Engineering Science, Osaka University, Toyonaka, Japan

  Masanobu Taniguchi

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