Author | Taniguchi, Masanobu. author |
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Title | Asymptotic Theory of Statistical Inference for Time Series [electronic resource] / by Masanobu Taniguchi, Yoshihide Kakizawa |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1162-4 |
Descript | XVII, 662 p. online resource |
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 LeCamโs 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 Numerical Examples -- 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