Asymptotic Theory of Statistical Inference for Time Series
(Sprache: Englisch)
The primary aims of this book are to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA and ARMA processes. A wide variety of stochastic processes, e.g.,...
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Klappentext zu „Asymptotic Theory of Statistical Inference for Time Series “
The primary aims of this book are to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA and ARMA processes. A wide variety of stochastic processes, e.g., non-Gaussian linear processes, long-memory processes, non-linear processes, non-ergodic processes and diffusion processes are described. The authors discuss the usual estimation and testing theory and also many other statistical methods and techniques, e.g., discriminant analysis, nonparametric methods, semi-parametric approaches, higher order asymptotic theory in view of differential geometry, large deviation principle and saddlepoint approximation. Because it is difficult to use the exact distribution theory, the discussion is based on the asymptotic theory. The optimality of various procedures is often shown by use of the local asymptotic normality (LAN) which is due to Le Cam. The LAN givesa unified view for the time seriesasym ptotic theory.
Inhaltsverzeichnis zu „Asymptotic Theory of Statistical Inference for Time Series “
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.- 3.1.1 Asymptotic Theory Based on a Gaussian Likelihood.- 3.1.2 Asymptotic Theory of Estimation and Testing Based on LAN Results.- 3.2 Asymptotic Theory for Nonlinear Stochastic Models.- 3.2.1 Nonlinear Models.- 3.2.2 Probability Structure of Nonlinear Models.- 3.2.3 Statistical Testing and Estimation Theory for Nonlinear Models.- 3.2.4 Asymptotic Theory Based on the LAN Property.- 3.2.5 Model Selection Problems.- 3.2.6 Nonergodic Models.- 3.3 Asymptotic Theory for Continuous Time Processes.- 3.3.1 Stochastic Integrals and Diffusion Processes.- 3.3.2 Asymptotic Theory for Diffusion Processes.- 3.3.3 Diffusion Processes and Autoregressions with Roots.- Near Unity.- 3.3.4 Continuous Time ARMA Processes.- 3.3.5 Asymptotic Theory for Point 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
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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.- 6.4.1 Robustness to Small Trends of Linear Functionals of a Periodogram.- 6.4.2 Peak-Insensitive Spectrum Estimation.- 6.5 Numerical Examples.- Problems.- 7 Discriminant Analysis for Stationary Time Series.- 7.1 Basic Formulation.- 7.2 Standard Methods for Gaussian Stationary Processes.- 7.2.1 Time Domain Methods.- 7.2.2 Frequency Domain Methods.- 7.2.3 Admissible Linear Procedure: Case of Unequal Mean Vectors and Covariance Matrices.- 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.- 8.2.1 Asymptotic Theory of Neyman-Pearson Tests.- 8.2.2 Bahadur Efficiency of Estimator.- 8.2.3 Stochastic Comparison of Tests.- 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.
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Bibliographische Angaben
- Autoren: Masanobu Taniguchi , Yoshihide Kakizawa
- 2000, 2000, 662 Seiten, Masse: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387950397
- ISBN-13: 9780387950396
- Erscheinungsdatum: 11.08.2000
Sprache:
Englisch
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