Asymptotic Theory of Statistical Inference for Time Series

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...

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Bibliographic Details
Main Authors: Taniguchi, Masanobu, Kakizawa, Yoshihide (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 2000, 2000
Edition:1st ed. 2000
Series:Springer Series in Statistics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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