時(shí)間序列分析及其應(yīng)用

前言

The goals of this book are to develop an appreciation for the richness andversatility of modern time series analysis as a tool for analyzing data, and stillmaintain a commitment to theoretical integrity, as exemplified by the seminalworks of Brillinger （1981） and Hannan （1970） and the texts by Brockwell andDavis （1991） and Fuller （1995）. The advent of more powerful computing, es-pecially in the last three years, has provided both real data and new softwarethat can take one considerably beyond the fitting of simple time domain mod-els, such as have been elegantly described in the landmark work of Box andJenkins （see Box et al., 1994）. This book is designed to be useful as a textfor courses in time series on several different levels and as a reference workfor practitioners facing the analysis of time-correlated data in the physical,biological, and social sciences.We believe the book will be useful as a text at both the undergraduate andgraduate levels. An undergraduate course can be accessible to students with abackground in regression analysis and might include Sections 1.1-1.8, 2.1-2.9,and 3.1-3.8. Similar courses have been taught at the University of California（Berkeley and Davis） in the past using the earlier book on applied time seriesanalysis by Shumway （1988）. Such a course is taken by undergraduate studentsin mathematics, economics, and statistics and attracts graduate students fromthe agricultural, biological, and environmental sciences. At the master's degreelevel, it can be useful to students in mathematics, environmental science, eco-nomics, statistics, and engineering by adding Sections 1.9, 2.10-2.14, 3.9, 3.10,4.1-4.5, to those proposed above. Finally, a two-semester upper-level graduatecourse for mathematics, statistics and engineering graduate students can becrafted by adding selected theoretical sections from the last sections of Chap-ters 1, 2, and 3 for mathematics and statistics students and some advancedapplications from Chapters 4 and 5. For the upper-level graduate course, weshould mention that we are striving for a less rigorous level of coverage thanthat which is attained by Brockwell and Davis （1991）, the classic entry at thislevel.

內(nèi)容概要

　　The goals of this book are to develop an appreciation for the richness andversatility of modern time series analysis as a tool for analyzing data， and stillmaintain a commitment to theoretical integrity， as exemplified by the seminalworks of Brillinger （1981） and Hannan （1970） and the texts by Brockwell andDavis （1991） and Fuller （1995）. The advent of more powerful computing， es-pecially in the last three years， has provided both real data and new softwarethat can take one considerably beyond the fitting of simple time domain mod-els， such as have been elegantly described in the landmark work of Box andJenkins （see Box et al.， 1994）. This book is designed to be useful as a textfor courses in time series on several different levels and as a reference workfor practitioners facing the analysis of time-correlated data in the physical，biological， and social sciences.

作者簡介

作者：(美國) 羅伯特沙姆韋 (Shumway.R.H.)

書籍目錄

1  Characteristics of Time Series  1.1  Introduction  1.2  The Nature of Time Series Data  1.3  Time Series Statistical Models  1.4  Measures of Dependence: Autocorrelation and Cross-Correlation  1.5  Stationary Time Series  1.6  Estimation of Correlation  1.7  Vector-Valued and Multidimensional Series  Problems2  Time Series Regression and Exploratory Data Analysis  2.1  Introduction  2.2  Classical Regression in the Time Series Context  2.3  Exploratory Data Analysis  2.4  Smoothing in the Time Series Context  Problems3  ARIMA Models  3.1  Introduction    3.2  Autoregressive Moving Average Models  3.3  Difference Equations  3.4  Autocorrelation and Partial Autocorrelation Functions   3.5  Forecasting  3.6  Estimation  3.7  Integrated Models for Nonstationary Data  3.8  Building ARIMA Models  3.9  Multiplicative Seasonal ARIMA Models  Problems4  Spectral Analysis and Filtering  4.1  Introduction  4.2  Cyclical Behavior and Periodicity  4.3  The Spectral Density  4.4  Periodogram and Discrete Fourier Transform  4.5  Nonparametric Spectral Estimation  4.6  Multiple Series and Cross-Spectra  4.7  Linear Filters  4.8  Parametric Spectral Estimation  4.9  Dynamic Fourier Analysis and Wavelets  4.10 Lagged Regression Models  4.11 Signal Extraction and Optimum Filtering  4.12 Spectral Analysis of Multidimensional Series  Problems5  Additional Time Domain Topics  5.1  Introduction  5.2  Long Memory ARMA and Fractional Differencing  5.3  GARCH Models  5.4  Threshold Models  5.5  Regression with Autocorrelated Errors  5.6  Lagged Regression: Transfer Function Modeling  5.7  Multivariate ARMAX Models  Problems6  State-Space Models  6.1  Introduction  6.2  Filtering, Smoothing, and Forecasting  6.3  Maximum Likelihood Estimation  6.4  Missing Data Modifications  6.5  Structural Models: Signal Extraction and Forecasting    6.6  ARMAX Models in State-Space Form  6.7  Bootstrapping State-Space Models  6.8  Dynamic Linear Models with Switching  6.9  Nonlinear and Non-normal State-Space Models Using Monte Carlo Methods  6.10 Stochastic Volatility  6.11 State-Space and ARMAX Models for Longitudinal Data Analysis  Problems7  Statistical Methods in the Frequency Domain  7.1  Introduction  7.2  Spectral Matrices and Likelihood Functions  7.3  Regression for Jointly Stationary Series  7.4  Regression with Deterministic Inputs  7.5  Random Coefficient Regression  7.6  Analysis of Designed Experiments  7.7  Discrimination and Cluster Analysis  7.8  Principal Components and Factor Analysis  7.9  The Spectral Envelope  ProblemsAppendix A: Large Sample Theory  A.1  Convergence Modes  A.2  Central Limit Theorems  A.3  The Mean and Autocorrelation FunctionsAppendix B: Time Domain Theory  B.1  Hilbert Spaces and the Projection Theorem  B.2  Causal Conditions for ARMA Models  B.3  Large Sample Distribution of the AR(p) Conditional Least Squares Estimators  B.4  The Wold DecompositionAppendix C: Spectral Domain Theory  C.1  Spectral Representation Theorem  C.2  Large Sample Distribution of the DFT and Smoothed Periodogram  C.3  The Complex Multivariate Normal Distribution ReferencesIndex

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