04107nmm a2200277 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002400139245010800163250001700271260004800288300003300336505163800369653002402007653002802031653003202059041001902091989003802110490003202148856007202180082000802252520156902260EB000619401EBX0100000000000000047248300000000000000.0cr|||||||||||||||||||||140122 ||| eng a97814612315471 aTaniguchi, Masanobu00aHigher Order Asymptotic Theory for Time Series AnalysishElektronische Ressourcecby Masanobu Taniguchi a1st ed. 1991 aNew York, NYbSpringer New Yorkc1991, 1991 aVIII, 160 pbonline resource0 a1 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 aApplied mathematics aEngineering mathematics aApplications of Mathematics07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aLecture Notes in Statistics40uhttps://doi.org/10.1007/978-1-4612-3154-7?nosfx=yxVerlag3Volltext0 a519 aThe 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 MulĀ 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