Asymptotic Theory of Statistical Inference for Time Series
Published on 11. August 2000
Book
Hardback
XVII, 662 pages
978-0-387-95039-6 (ISBN)
Description
There has been much demand for the statistical analysis of dependent ob servations in many fields, for example, economics, engineering and the nat ural sciences. A model that describes the probability structure of a se ries of dependent observations is called a stochastic process. The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes. We deal with a wide variety of stochastic processes, for example, non-Gaussian linear processes, long-memory processes, nonlinear processes, orthogonal increment process es, and continuous time processes. For them we develop not only the usual estimation and testing theory but also many other statistical methods and techniques, such as discriminant analysis, cluster analysis, nonparametric methods, higher order asymptotic theory in view of differential geometry, large deviation principle, and saddlepoint approximation. Because it is d ifficult to use the exact distribution theory, the discussion is based on the asymptotic theory. Optimality of various procedures is often shown by use of local asymptotic normality (LAN), which is due to LeCam. This book is suitable as a professional reference book on statistical anal ysis of stochastic processes or as a textbook for students who specialize in statistics. It will also be useful to researchers, including those in econo metrics, mathematics, and seismology, who utilize statistical methods for stochastic processes.
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From the reviews:
MATHEMATICAL REVIEWS
"It is valuable both as an advanced graduate level text and as a reference for researchers?he book can be most strongly recommended."
More details
Series
Edition
2000 ed.
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
XVII, 662 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 41 mm
Weight
1180 gr
ISBN-13
978-0-387-95039-6 (9780387950396)
DOI
10.1007/978-1-4612-1162-4
Schweitzer Classification
Other editions
Additional editions
Masanobu Taniguchi | Yoshihide Kakizawa
Asymptotic Theory of Statistical Inference for Time Series
Book
10/2012
Springer
€181.89
Shipment within 15-20 days
Persons
Yuichi Goto is an assistant professor in Department of Mathematical Sciences, Faculty of Mathematics at Kyushu University. He earned his Ph.D. from Waseda University in 2021 and he was an assistant professor in Waseda University for one year. He completed a master's course in one year (one year early) and a doctor's course in two years (one year early). His research interests include time series analysis, especially frequency domain analysis, integer-valued time series, and analysis of variance. He received the Azusa Ono Memorial Award in 2021 and IMS New Researcher Travel Awards in 2023.
Hideaki Nagahata is a project assistant professor in Risk Analysis Research Center at the Institute of Statistical Mathematics. His research interests include multivariate time series analysis and quantitative aspects of risk modelling. He has worked on the estimation of loss given default (LGD) with local banks and quantifying the risk of compensation triggered on the CompoundLivestock Feed Supply Stabilization System with the Ministry of Agriculture, Forestry, and Fisheries.
Masanobu Taniguchi is an Emeritus professor at Waseda University. His research interests include time series analysis, mathematical statistics, multivariate analysis, information geometry, signal processing, econometric theory, and financial engineering. His main contributions in time series analysis are collected in his book: "Asymptotic Theory of Statistical Inference for Time Series" (New York : Springer-Verlag, 2000). He received the Ogawa Prize (Japan) in 1989, the Econometric Theory Award (USA) in 2000, the Japan Statistical Society Prize in 2004, Analysis Award in 2013 (Mathematical Society of Japan), Award of Japanese Minister of Education, Culture, Sports, Science & Technology in 2022, and the Distinguished Author Award in 2020 (Journal of Time Series Analysis, UK). He is a fellow of the Institute of Mathematical Statistics (USA, 1987 - ).
Anna Clara Monti is a professor in the Department of Law, Economics, Management, and Quantitative Methods at University of Sannio. She acted as dean of the Faculty of Economics and the Faculty of Law. Her research interests concern statistical inference, robustness, ordinal response models, and time series. She has published several papers in international journals of statistics, e.g. Biometrika, JRSS(B), JASA, etc.
Xiaofei Xu is an assistant professor in School of Mathematics and Statistics at Wuhan University. Before joining Wuhan University, she worked as an assistant professor in Waseda Unversity. She got Ph.D. degree in statistics in 2020. Her research interests include functional data analysis, count time series analysis, non-stationarity and high dimensionality, and energy forecasting. Xiaofei has published several papers in famous international journals including Annals of Applied Statistics and Journal of Business and Economic Statistics.
Content
1 Elements of Stochastic Processes.- 1.1 Introduction.- 1.2 Stochastic Processes.- 1.3 Limit Theorems.- Problems.- 2 Local Asymptotic Normality for Stochastic Processes.- 2.1 General Results for Local Asymptotic Normality.- 2.2 Local Asymptotic Normality for Linear Processes.- Problems.- 3 Asymptotic Theory of Estimation and Testing for Stochastic Processes.- 3.1 Asymptotic Theory of Estimation and Testing for Linear Processes.- 3.2 Asymptotic Theory for Nonlinear Stochastic Models.- 3.3 Asymptotic Theory for Continuous Time Processes.- Problems.- 4 Higher Order Asymptotic Theory for Stochastic Processes.- 4.1 Introduction to Higher Order Asymptotic Theory.- 4.2 Valid Asymptotic Expansions.- 4.3 Higher Order Asymptotic Estimation Theory for Discrete Time Processes in View of Statistical Differential Geometry.- 4.4 Higher Order Asymptotic Theory for Continuous Time Processes.- 4.5 Higher Order Asymptotic Theory for Testing Problems.- 4.6 Higher Order Asymptotic Theory for Normalizing Transformations.- 4.7 Generalization of LeCam's Third Lemma and Higher Order Asymptotics of Iterative Methods.- Problems.- 5 Asymptotic Theory for Long-Memory Processes.- 5.1 Some Elements of Long-Memory Processes.- 5.2 Limit Theorems for Fundamental Statistics.- 5.3 Estimation and Testing Theory for Long-Memory Processes.- 5.4 Regression Models with Long-Memory Disturbances.- 5.5 Semiparametric Analysis and the LAN Approach.- Problems.- 6 Statistical Analysis Based on Functionals of Spectra.- 6.1 Estimation of Nonlinear Functionals of Spectra.- 6.2 Application to Parameter Estimation for Stationary Processes.- 6.3 Asymptotically Efficient Nonparametric Estimation of Functionals of Spectra in Gaussian Stationary Processes.- 6.4 Robustness in the Frequency Domain Approach.- 6.5 NumericalExamples.- Problems.- 7 Discriminant Analysis for Stationary Time Series.- 7.1 Basic Formulation.- 7.2 Standard Methods for Gaussian Stationary Processes.- 7.3 Discriminant Analysis for Non-Gaussian Linear Processes.- 7.4 Nonparametric Approach for Discriminant Analysis.- 7.5 Parametric Approach for Discriminant Analysis.- 7.6 Derivation of Spectral Expressions to Divergence Measures Between Gaussian Stationary Processes.- 7.7 Miscellany.- Problems.- 8 Large Deviation Theory and Saddlepoint Approximation for Stochastic Processes.- 8.1 Large Deviation Theorem 538 8.2 Asymptotic Efficiency for Gaussian Stationary Processes:Large Deviation Approach.- 8.3 Large Deviation Results for an Ornstein-Uhlenbeck Process.- 8.4 Saddlepoint Approximations for Stochastic Processes.- Problems.- A.1 Mathematics.- A.2 Probability.- A.3 Statistics.