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非线性时间序列—建模、预报及应用

样章
作者：
范剑青 姚琦伟
定价：
79.00 元
版面字数：
670.00千字
开本：
16开
装帧形式：
精装
页数：
440
最新
印次时间：
2023年01月
ISBN：
978-7-04-017357-4
物料号：
17357-00
出版时间：
2006-01-10
读者对象：
学术著作
一级分类：
自然科学
二级分类：
统计学
三级分类：
统计理论和方法

本书主要介绍非线性时间序列理论和方法的一些最新研究成果，尤其以近十年来发展起来的非参数和半参数技术为主。 本书不仅对这些技术在时间序列状态空间、频域和时域等方面的应用给出了详细的介绍。同时，为了体现参数和非参数方法在时间序列分析中的整合性，还系统地阐述了一些主要参数非线性时间序列模型（比如ARCH/GARCH模型和门限模型等）的近期研究成果。此外，书中还包含了一个对线性ARMA模型的简洁介绍。为了说明如何运用非参数技术来揭示高维数据的局部结构，本书借助了很多源于实际问题的具体数据，并注重在这些例子的分析中体现部分的分析技巧和工具，阅读本书只需要具备基础的概率论和统计学知识。

本书适用于统计专业的研究生面向应用的时间序列分析人员以及该领域的各类研究人员。此外，本书也对从事统计学的其他分支以及经济计量学、实证金融学、总体生物和生态学的研究人员有参考价值。

  • 目录
    • front matter
      • 1 Introduction
        • 1.1 Examples of Time Series
          • 1.2 Objectives of Time Series Analysis
            • 1.3 Linear Time Series Models
              • 1.3.1 White Noise Processes
                • 1.3.2 AR Models
                  • 1.3.3 MA Models
                    • 1.3.4 ARMA Models
                      • 1.3.5 ARIMA Models
                      • 1.4 What Is a Nonlinear Time Series?
                        • 1.5 Nonlinear Time Series Models
                          • 1.5.1 A Simple Example
                            • 1.5.2 ARCH Models
                              • 1.5.3 Threshold Models
                                • 1.5.4 Nonparametric Autoregressive Models
                                • 1.6 From Linear to Nonlinear Models
                                  • 1.6.1 Local Linear Modeling
                                    • 1.6.2 Global Spline Approximation
                                      • 1.6.3 Goodness-of-Fit Tests
                                      • 1.7 Further Reading
                                        • 1.8 Software Implementations
                                        • 2 Characterlstics of Time Series
                                          • 2.1 Stationarity
                                            • 2.1.1 Definition
                                              • 2.1.2 Stationary ARMA Processes
                                                • 2.1.3 Stationary Gaussian Processes
                                                  • 2.1.4 Ergodic Nonlinear Models∗
                                                    • 2.1.5 Stationary ARCH Processes
                                                    • 2.2 Autocorrelation
                                                      • 2.2.1 Autocovariance and Autocorrelation
                                                        • 2.2.2 Estimation of ACVF and ACF
                                                          • 2.2.3 Partial Autocorrelation
                                                            • 2.2.4 ACF Plots, PACF Plots, and Examples
                                                            • 2.3 Spectral Distributions
                                                              • 2.3.1 Periodic Processes
                                                                • 2.3.2 Spectral Densities
                                                                  • 2.3.3 Linear Filters
                                                                  • 2.4 Periodogram
                                                                    • 2.4.1 Discrete Fourier Transforms
                                                                      • 2.4.2 Periodogram
                                                                      • 2.5 Long-Memory Processes∗
                                                                        • 2.5.1 Fractionally Integrated Noise
                                                                          • 2.5.2 Fractionally Integrated ARMA processes
                                                                          • 2.6 Mixing∗
                                                                            • 2.6.1 Mixing Conditions
                                                                              • 2.6.2 Inequalities
                                                                                • 2.6.3 Limit Theorems for α-Mixing Processes
                                                                                  • 2.6.4 A Central Limit Theorem for Nonparametric Regression
                                                                                  • 2.7 Complements
                                                                                    • 2.7.1 Proof of Theorem 2.5(i)
                                                                                      • 2.7.2 Proof of Proposition 2.3(i)
                                                                                        • 2.7.3 Proof of Theorem 2.9
                                                                                          • 2.7.4 Proof of Theorem 2.10
                                                                                            • 2.7.5 Proof of Theorem 2.13
                                                                                              • 2.7.6 Proof of Theorem 2.14
                                                                                                • 2.7.7 Proof of Theorem 2.22
                                                                                                • 2.8 Additional Bibliographical Notes
                                                                                                • 3 ARMA Modeling and Forecasting
                                                                                                  • 3.1 Models and Background
                                                                                                    • 3.2 The Best Linear Prediction—Prewhitening
                                                                                                      • 3.3 Maximum Likelihood Estimation
                                                                                                        • 3.3.1 Estimators
                                                                                                          • 3.3.2 Asymptotic Properties
                                                                                                            • 3.3.3 Confidence Intervals
                                                                                                            • 3.4 Order Determination
                                                                                                              • 3.4.1 Akaike Information Criterion
                                                                                                                • 3.4.2 FPE Criterion for AR Modeling
                                                                                                                  • 3.4.3 Bayesian Information Criterion
                                                                                                                    • 3.4.4 Model Identification
                                                                                                                    • 3.5 Diagnostic Checking
                                                                                                                      • 3.5.1 Standardized Residuals
                                                                                                                        • 3.5.2 Visual Diagnostic
                                                                                                                          • 3.5.3 Tests for Whiteness
                                                                                                                          • 3.6 A Real Data Example—Analyzing German Egg Prices
                                                                                                                            • 3.7 Linear Forecasting
                                                                                                                              • 3.7.1 The Least Squares Predictors
                                                                                                                                • 3.7.2 Forecasting in AR Processes
                                                                                                                                  • 3.7.3 Mean Squared Predictive Errors for AR Processes
                                                                                                                                    • 3.7.4 Forecasting in ARMA Processes
                                                                                                                                  • 4 Parametric Nonlinear Time Series Models
                                                                                                                                    • 4.1 Threshold Models
                                                                                                                                      • 4.1.1 Threshold Autoregressive Models
                                                                                                                                        • 4.1.2 Estimation and Model Identification
                                                                                                                                          • 4.1.3 Tests for Linearity
                                                                                                                                            • 4.1.4 Case Studies with Canadian Lynx Data
                                                                                                                                            • 4.2 ARCH and GARCH Models
                                                                                                                                              • 4.2.1 Basic Properties of ARCH Processes
                                                                                                                                                • 4.2.2 Basic Properties of GARCH Processes
                                                                                                                                                  • 4.2.3 Estimation
                                                                                                                                                    • 4.2.4 Asymptotic Properties of Conditional MLEs∗
                                                                                                                                                      • 4.2.5 Bootstrap Confidence Intervals
                                                                                                                                                        • 4.2.6 Testing for the ARCH Effect
                                                                                                                                                          • 4.2.7 ARCH Modeling of Financial Data
                                                                                                                                                            • 4.2.8 A Numerical Example: Modeling S&P 500 Index Returns
                                                                                                                                                              • 4.2.9 Stochastic Volatility Models
                                                                                                                                                              • 4.3 Bilinear Models
                                                                                                                                                                • 4.3.1 A Simple Example
                                                                                                                                                                  • 4.3.2 Markovian Representation
                                                                                                                                                                    • 4.3.3 Probabilistic Properties∗
                                                                                                                                                                      • 4.3.4 Maximum Likelihood Estimation
                                                                                                                                                                        • 4.3.5 Bispectrum
                                                                                                                                                                        • 4.4 Additional Bibliographical notes
                                                                                                                                                                        • 5 Nonparametric Density Estimation
                                                                                                                                                                          • 5.1 Introduction
                                                                                                                                                                            • 5.2 Kernel Density Estimation
                                                                                                                                                                              • 5.3 Windowing and Whitening
                                                                                                                                                                                • 5.4 Bandwidth Selection
                                                                                                                                                                                  • 5.5 Boundary Correction
                                                                                                                                                                                    • 5.6 Asymptotic Results∗
                                                                                                                                                                                      • 5.7 Complements—Proof of Theorem 5.3
                                                                                                                                                                                        • 5.8 Bibliographical Notes
                                                                                                                                                                                        • 6 Smoothing in Time Series
                                                                                                                                                                                          • 6.1 Introduction
                                                                                                                                                                                            • 6.2 Smoothing in the Time Domain
                                                                                                                                                                                              • 6.2.1 Trend and Seasonal Components
                                                                                                                                                                                                • 6.2.2 Moving Averages
                                                                                                                                                                                                  • 6.2.3 Kernel Smoothing
                                                                                                                                                                                                    • 6.2.4 Variations of Kernel Smoothers
                                                                                                                                                                                                      • 6.2.5 Filtering
                                                                                                                                                                                                        • 6.2.6 Local Linear Smoothing
                                                                                                                                                                                                          • 6.2.7 Other Smoothing Methods
                                                                                                                                                                                                            • 6.2.8 Seasonal Adjustments
                                                                                                                                                                                                              • 6.2.9 Theoretical Aspects∗
                                                                                                                                                                                                              • 6.3 Smoothing in the State Domain
                                                                                                                                                                                                                • 6.3.1 Nonparametric Autoregression
                                                                                                                                                                                                                  • 6.3.2 Local Polynomial Fitting
                                                                                                                                                                                                                    • 6.3.3 Properties of the Local Polynomial Estimator
                                                                                                                                                                                                                      • 6.3.4 Standard Errors and Estimated Bias
                                                                                                                                                                                                                        • 6.3.5 Bandwidth Selection
                                                                                                                                                                                                                        • 6.4 Spline Methods
                                                                                                                                                                                                                          • 6.4.1 Polynomial splines
                                                                                                                                                                                                                            • 6.4.2 Nonquadratic Penalized Splines
                                                                                                                                                                                                                              • 6.4.3 Smoothing Splines
                                                                                                                                                                                                                              • 6.5 Estimation of Conditional Densities
                                                                                                                                                                                                                                • 6.5.1 Methods of Estimation
                                                                                                                                                                                                                                  • 6.5.2 Asymptotic Properties∗
                                                                                                                                                                                                                                  • 6.6 Complements
                                                                                                                                                                                                                                    • 6.6.1 Proof of Theorem 6.1
                                                                                                                                                                                                                                      • 6.6.2 Conditions and Proof of Theorem 6.3
                                                                                                                                                                                                                                        • 6.6.3 Proof of Lemma 6.1
                                                                                                                                                                                                                                          • 6.6.4 Proof of Theorem 6.5
                                                                                                                                                                                                                                            • 6.6.5 Proof for Theorems 6.6 and 6.7
                                                                                                                                                                                                                                            • 6.7 Bibliographical Notes
                                                                                                                                                                                                                                            • 7 Spectral Density Estimation and Its Applications
                                                                                                                                                                                                                                              • 7.1 Introduction
                                                                                                                                                                                                                                                • 7.2 Tapering, Kernel Estimation, and Prewhitening
                                                                                                                                                                                                                                                  • 7.2.1 Tapering
                                                                                                                                                                                                                                                    • 7.2.2 Smoothing the Periodogram
                                                                                                                                                                                                                                                      • 7.2.3 Prewhitening and Bias Reduction
                                                                                                                                                                                                                                                      • 7.3 Automatic Estimation of Spectral Density
                                                                                                                                                                                                                                                        • 7.3.1 Least-Squares Estimators and Bandwidth Selection
                                                                                                                                                                                                                                                          • 7.3.2 Local Maximum Likelihood Estimator
                                                                                                                                                                                                                                                            • 7.3.3 Confidence Intervals
                                                                                                                                                                                                                                                            • 7.4 Tests for White Noise
                                                                                                                                                                                                                                                              • 7.4.1 Fisher’s Test
                                                                                                                                                                                                                                                                • 7.4.2 Generalized Likelihood Ratio Test
                                                                                                                                                                                                                                                                  • 7.4.3 χ2-Test and the Adaptive Neyman Test
                                                                                                                                                                                                                                                                    • 7.4.4 Other Smoothing-Based Tests
                                                                                                                                                                                                                                                                      • 7.4.5 Numerical Examples
                                                                                                                                                                                                                                                                      • 7.5 Complements
                                                                                                                                                                                                                                                                        • 7.5.1 Conditions for Theorems 7.1—7.3
                                                                                                                                                                                                                                                                          • 7.5.2 Lemmas
                                                                                                                                                                                                                                                                            • 7.5.3 Proof of Theorem 7.1
                                                                                                                                                                                                                                                                              • 7.5.4 Proof of Theorem 7.2
                                                                                                                                                                                                                                                                                • 7.5.5 Proof of Theorem 7.3
                                                                                                                                                                                                                                                                                • 7.6 Bibliographical Notes
                                                                                                                                                                                                                                                                                • 8 Nonparametric Models
                                                                                                                                                                                                                                                                                  • 8.1 Introduction
                                                                                                                                                                                                                                                                                    • 8.2 Multivariate Local Polynomial Regression
                                                                                                                                                                                                                                                                                      • 8.2.1 Multivariate Kernel Functions
                                                                                                                                                                                                                                                                                        • 8.2.2 Multivariate Local Linear Regression
                                                                                                                                                                                                                                                                                          • 8.2.3 Multivariate Local Quadratic Regression
                                                                                                                                                                                                                                                                                          • 8.3 Functional-Coefficient Autoregressive Model
                                                                                                                                                                                                                                                                                            • 8.3.1 The Model
                                                                                                                                                                                                                                                                                              • 8.3.2 Relation to Stochastic Regression
                                                                                                                                                                                                                                                                                                • 8.3.3 Ergodicity∗
                                                                                                                                                                                                                                                                                                  • 8.3.4 Estimation of Coefficient Functions
                                                                                                                                                                                                                                                                                                    • 8.3.5 Selection of Bandwidth and Model-Dependent Variable
                                                                                                                                                                                                                                                                                                      • 8.3.6 Prediction
                                                                                                                                                                                                                                                                                                        • 8.3.7 Examples
                                                                                                                                                                                                                                                                                                          • 8.3.8 Sampling Properties∗
                                                                                                                                                                                                                                                                                                          • 8.4 Adaptive Functional-Coefficient Autoregressive Models
                                                                                                                                                                                                                                                                                                            • 8.4.1 The Models
                                                                                                                                                                                                                                                                                                              • 8.4.2 Existence and Identifiability
                                                                                                                                                                                                                                                                                                                • 8.4.3 Profile Least-Squares Estimation
                                                                                                                                                                                                                                                                                                                  • 8.4.4 Bandwidth Selection
                                                                                                                                                                                                                                                                                                                    • 8.4.5 Variable Selection
                                                                                                                                                                                                                                                                                                                      • 8.4.6 Implementation
                                                                                                                                                                                                                                                                                                                        • 8.4.7 Examples
                                                                                                                                                                                                                                                                                                                          • 8.4.8 Extensions
                                                                                                                                                                                                                                                                                                                          • 8.5 Additive Models
                                                                                                                                                                                                                                                                                                                            • 8.5.1 The Models
                                                                                                                                                                                                                                                                                                                              • 8.5.2 The Backfitting Algorithm
                                                                                                                                                                                                                                                                                                                                • 8.5.3 Projections and Average Surface Estimators
                                                                                                                                                                                                                                                                                                                                  • 8.5.4 Estimability of Coefficient Functions
                                                                                                                                                                                                                                                                                                                                    • 8.5.5 Bandwidth Selection
                                                                                                                                                                                                                                                                                                                                      • 8.5.6 Examples
                                                                                                                                                                                                                                                                                                                                      • 8.6 Other Nonparametric Models
                                                                                                                                                                                                                                                                                                                                        • 8.6.1 Two-Term Interaction Models
                                                                                                                                                                                                                                                                                                                                          • 8.6.2 Partially Linear Models
                                                                                                                                                                                                                                                                                                                                            • 8.6.3 Single-Index Models
                                                                                                                                                                                                                                                                                                                                              • 8.6.4 Multiple-Index Models
                                                                                                                                                                                                                                                                                                                                                • 8.6.5 An Analysis of Environmental Data
                                                                                                                                                                                                                                                                                                                                                • 8.7 Modeling Conditional Variance
                                                                                                                                                                                                                                                                                                                                                  • 8.7.1 Methods of Estimating Conditional Variance
                                                                                                                                                                                                                                                                                                                                                    • 8.7.2 Univariate Setting
                                                                                                                                                                                                                                                                                                                                                      • 8.7.3 Functional-Coefficient Models
                                                                                                                                                                                                                                                                                                                                                        • 8.7.4 Additive Models
                                                                                                                                                                                                                                                                                                                                                          • 8.7.5 Product Models
                                                                                                                                                                                                                                                                                                                                                            • 8.7.6 Other Nonparametric Models
                                                                                                                                                                                                                                                                                                                                                            • 8.8 Complements
                                                                                                                                                                                                                                                                                                                                                              • 8.8.1 Proof of Theorem 8.1
                                                                                                                                                                                                                                                                                                                                                                • 8.8.2 Technical Conditions for Theorems 8.2 and 8.3
                                                                                                                                                                                                                                                                                                                                                                  • 8.8.3 Preliminaries to the Proof of Theorem 8.3
                                                                                                                                                                                                                                                                                                                                                                    • 8.8.4 Proof of Theorem 8.3
                                                                                                                                                                                                                                                                                                                                                                      • 8.8.5 Proof of Theorem 8.4
                                                                                                                                                                                                                                                                                                                                                                        • 8.8.6 Conditions of Theorem 8.5
                                                                                                                                                                                                                                                                                                                                                                          • 8.8.7 Proof of Theorem 8.5
                                                                                                                                                                                                                                                                                                                                                                          • 8.9 Bibliographical Notes
                                                                                                                                                                                                                                                                                                                                                                          • 9 Model Validation
                                                                                                                                                                                                                                                                                                                                                                            • 9.1 Introduction
                                                                                                                                                                                                                                                                                                                                                                              • 9.2 Generalized Likelihood Ratio Tests
                                                                                                                                                                                                                                                                                                                                                                                • 9.2.1 Introduction
                                                                                                                                                                                                                                                                                                                                                                                  • 9.2.2 Generalized Likelihood Ratio Test
                                                                                                                                                                                                                                                                                                                                                                                    • 9.2.3 Null Distributions and the Bootstrap
                                                                                                                                                                                                                                                                                                                                                                                      • 9.2.4 Power of the GLR Test
                                                                                                                                                                                                                                                                                                                                                                                        • 9.2.5 Bias Reduction
                                                                                                                                                                                                                                                                                                                                                                                          • 9.2.6 Nonparametric versus Nonparametric Models
                                                                                                                                                                                                                                                                                                                                                                                            • 9.2.7 Choice of Bandwidth
                                                                                                                                                                                                                                                                                                                                                                                              • 9.2.8 A Numerical Example
                                                                                                                                                                                                                                                                                                                                                                                              • 9.3 Tests on Spectral Densities
                                                                                                                                                                                                                                                                                                                                                                                                • 9.3.1 Relation with Nonparametric Regression
                                                                                                                                                                                                                                                                                                                                                                                                  • 9.3.2 Generalized Likelihood Ratio Tests
                                                                                                                                                                                                                                                                                                                                                                                                    • 9.3.3 Other Nonparametric Methods
                                                                                                                                                                                                                                                                                                                                                                                                      • 9.3.4 Tests Based on Rescaled Periodogram
                                                                                                                                                                                                                                                                                                                                                                                                      • 9.4 Autoregressive versus Nonparametric Models
                                                                                                                                                                                                                                                                                                                                                                                                        • 9.4.1 Functional-Coefficient Alternatives
                                                                                                                                                                                                                                                                                                                                                                                                          • 9.4.2 Additive Alternatives
                                                                                                                                                                                                                                                                                                                                                                                                          • 9.5 Threshold Models versus Varying-Coefficient Models
                                                                                                                                                                                                                                                                                                                                                                                                            • 9.6 Bibliographical Notes
                                                                                                                                                                                                                                                                                                                                                                                                            • 10 Nonlinear Prediction
                                                                                                                                                                                                                                                                                                                                                                                                              • 10.1 Features of Nonlinear Prediction
                                                                                                                                                                                                                                                                                                                                                                                                                • 10.1.1 Decomposition for Mean Square Predictive Errors
                                                                                                                                                                                                                                                                                                                                                                                                                  • 10.1.2 Noise Amplification
                                                                                                                                                                                                                                                                                                                                                                                                                    • 10.1.3 Sensitivity to Initial Values
                                                                                                                                                                                                                                                                                                                                                                                                                      • 10.1.4 Multiple-Step Prediction versus a One-Step Plug-in Method
                                                                                                                                                                                                                                                                                                                                                                                                                        • 10.1.5 Nonlinear versus Linear Prediction
                                                                                                                                                                                                                                                                                                                                                                                                                        • 10.2 Point Prediction
                                                                                                                                                                                                                                                                                                                                                                                                                          • 10.2.1 Local Linear Predictors
                                                                                                                                                                                                                                                                                                                                                                                                                            • 10.2.2 An Example
                                                                                                                                                                                                                                                                                                                                                                                                                            • 10.3 Estimating Predictive Distributions
                                                                                                                                                                                                                                                                                                                                                                                                                              • 10.3.1 Local Logistic Estimator
                                                                                                                                                                                                                                                                                                                                                                                                                                • 10.3.2 Adjusted Nadaraya-Watson Estimator
                                                                                                                                                                                                                                                                                                                                                                                                                                  • 10.3.3 Bootstrap Bandwidth Selection
                                                                                                                                                                                                                                                                                                                                                                                                                                    • 10.3.4 Numerical Examples
                                                                                                                                                                                                                                                                                                                                                                                                                                      • 10.3.5 Asymptotic Properties
                                                                                                                                                                                                                                                                                                                                                                                                                                        • 10.3.6 Sensitivity to Initial Values: A Conditional Distribution Approach
                                                                                                                                                                                                                                                                                                                                                                                                                                        • 10.4 Interval Predictors and Predictive Sets
                                                                                                                                                                                                                                                                                                                                                                                                                                          • 10.4.1 Minimum-Length Predictive Sets
                                                                                                                                                                                                                                                                                                                                                                                                                                            • 10.4.2. Estimation of Minimum-Length Predictors
                                                                                                                                                                                                                                                                                                                                                                                                                                              • 10.4.3 Numerical Examples
                                                                                                                                                                                                                                                                                                                                                                                                                                              • 10.5 Coomplements
                                                                                                                                                                                                                                                                                                                                                                                                                                                • 10.6 Additional Bibliographical Notes
                                                                                                                                                                                                                                                                                                                                                                                                                                                • References
                                                                                                                                                                                                                                                                                                                                                                                                                                                  • Index
                                                                                                                                                                                                                                                                                                                                                                                                                                                    • 版权

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