Ebook: Higher Order Asymptotic Theory for Time Series Analysis

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.

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This book gives higher order asymptotic results in time series analysis. Especially, higher order asymptotic optimality of estimators and power comparison of tests for ARMA processes are discussed. It covers higher order asymptotics of statistics of multivariate stationary processes. Numerical studies are given, and they show that the higher order asymptotic theory is useful and important for time series analysis. Also the validities of Edgeworth expansions of some estimators are proved for dependent situations. Many results will serve as the basis for the further theoretical development and their applications.

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This book gives higher order asymptotic results in time series analysis. Especially, higher order asymptotic optimality of estimators and power comparison of tests for ARMA processes are discussed. It covers higher order asymptotics of statistics of multivariate stationary processes. Numerical studies are given, and they show that the higher order asymptotic theory is useful and important for time series analysis. Also the validities of Edgeworth expansions of some estimators are proved for dependent situations. Many results will serve as the basis for the further theoretical development and their applications.
Content:
Front Matter....Pages I-VIII
A Survey of the First-Order Asymptotic Theory for Time Series Analysis....Pages 1-10
Higher Order Asymptotic Theory for Gaussian ARMA Processes....Pages 11-61
Validity of Edgeworth Expansions in Time Series Analysis....Pages 62-89
Higher Order Asymptotic Sufficiency, Asymptotic Ancillarity in Time Series Analysis....Pages 90-103
Higher Order Investigations for Testing Theory in Time Series Analysis....Pages 104-115
Higher Order Asymptotic Theory for Multivariate Time Series....Pages 116-128
Some Practical Examples....Pages 129-140
Back Matter....Pages 141-162

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This book gives higher order asymptotic results in time series analysis. Especially, higher order asymptotic optimality of estimators and power comparison of tests for ARMA processes are discussed. It covers higher order asymptotics of statistics of multivariate stationary processes. Numerical studies are given, and they show that the higher order asymptotic theory is useful and important for time series analysis. Also the validities of Edgeworth expansions of some estimators are proved for dependent situations. Many results will serve as the basis for the further theoretical development and their applications.
Content:
Front Matter....Pages I-VIII
A Survey of the First-Order Asymptotic Theory for Time Series Analysis....Pages 1-10
Higher Order Asymptotic Theory for Gaussian ARMA Processes....Pages 11-61
Validity of Edgeworth Expansions in Time Series Analysis....Pages 62-89
Higher Order Asymptotic Sufficiency, Asymptotic Ancillarity in Time Series Analysis....Pages 90-103
Higher Order Investigations for Testing Theory in Time Series Analysis....Pages 104-115
Higher Order Asymptotic Theory for Multivariate Time Series....Pages 116-128
Some Practical Examples....Pages 129-140
Back Matter....Pages 141-162
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