# Higher Order Asymptotic Theory for Time Series Analysis

• Masanobu Taniguchi
Book

Part of the Lecture Notes in Statistics book series (LNS, volume 68)

1. Front Matter
Pages I-VIII
2. Masanobu Taniguchi
Pages 1-10
3. Masanobu Taniguchi
Pages 11-61
4. Masanobu Taniguchi
Pages 62-89
5. Masanobu Taniguchi
Pages 90-103
6. Masanobu Taniguchi
Pages 104-115
7. Masanobu Taniguchi
Pages 116-128
8. Masanobu Taniguchi
Pages 129-140
9. Back Matter
Pages 141-162

### Introduction

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.

### Keywords

Covariance matrix Estimator Likelihood Time series Variance correlation

#### Authors and affiliations

• Masanobu Taniguchi
• 1
1. 1.Department of Mathematical Science, Faculty of Engineering ScienceOsaka UniversityToyonakaJapan

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-3154-7
• Copyright Information Springer-Verlag New York 1991
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-97546-7
• Online ISBN 978-1-4612-3154-7
• Series Print ISSN 0930-0325