Author	Taniguchi, Masanobu. author
Title	Higher Order Asymptotic Theory for Time Series Analysis [electronic resource] / by Masanobu Taniguchi
Imprint	New York, NY : Springer New York, 1991
Connect to	http://dx.doi.org/10.1007/978-1-4612-3154-7
Descript	VIII, 160 p. online resource

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 Mulยญ 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

1 A Survey of the First-Order Asymptotic Theory for Time Series Analysis -- 2 Higher Order Asymptotic Theory for Gaussian Arma Processes -- 2.1. Higher order asymptotic efficiency and Edgeworth expansions -- 2.2. Second-order asymptotic efficiency for Gaussian ARMA processes -- 2.3. Third-order asymptotic efficiency for Gaussian ARMA processes -- 2.4. Normalizing transformations of some statistics of Gaussian ARMA processes -- 2.5. Higher order asymptotic efficiency in time series regression models -- 3 Validity of Edgeworth Expansions in Time Series Analysis -- 3.1. Berry-Esseen theorems for quadratic forms of Gaussian stationary processes -- 3.2. Validity of Edgeworth expansions of generalized maximum likelihood estimators for Gaussian ARMA processes -- 4 Higher Order Asymptotic Sufficiency, Asymptotic Ancillarity in Time Series Analysis -- 4.1. Higher order asymptotic sufficiency for Gaussian ARMA processes -- 4.2. Asymptotic ancillarity in time series analysis -- 5 Higher Order Investigations for Testing Theory in Time Series Analysis -- 5.1. Asymptotic expansions of the distributions of a class of tests under the null hypothesis -- 5.2. Comparisons of powers of a class of tests under a local alternative -- 6 Higher Order Asymptotic Theory for Multivariate Time Series -- 6.1. Asymptotic expansions of the distributions of functions of the eigenvalues of sample covariance matrix in multivariate time series -- 6.2. Asymptotic expansions of the distributions of functions of the eigenvalues of canonical correlation matrix in multivariate time series -- 7 Some Practical Examples -- References -- Author Index

1. Mathematics
2. Applied mathematics
3. Engineering mathematics
4. Mathematics
5. Applications of Mathematics