時間序列分析

內(nèi)容概要

　　本書自1970年初版以來，不斷修訂再版，以其經(jīng)典性和權(quán)威性成為有關(guān)時間序列分析領(lǐng)域書籍的典范。書中涉及時間序列隨機(統(tǒng)計)模型的建立及許多重要的應用領(lǐng)域的使用，包括預測，模型的描述、估計、識別和診斷，動態(tài)關(guān)系的傳遞函數(shù)的識別、擬合及檢驗，干預事件影響的建模和過程控制等專題。本書敘述簡明，強調(diào)實際技術(shù)，配有大量實例。　　本書可作為統(tǒng)計和相關(guān)專業(yè)高年級本科生或研究生教材，也可以作為統(tǒng)計專業(yè)技術(shù)人員的參考書。

作者簡介

George E.P.Box 國際級統(tǒng)計學家。曾于1960年創(chuàng)立威斯康星大學統(tǒng)計系并任該系主任，現(xiàn)為該校名譽教授。BOX發(fā)表過200多篇論文，出版過很多重要著作，其中本書和STATISTICE FOR
EXPERIMENTERS為其代表作。
    Gwilym M.Jenkins 已故國際級統(tǒng)計學家。曾于1966年創(chuàng)立了英國

書籍目錄

1　INTRODUCTION　11.1　Four Important Practical Problems　21.1.1　Forecasting Time Series　21.1.2　Estimation of Transfer Functions　31.1.3　Analysis of Effects of Unusual Intervention Events To a System　41.1.4　Discrete Control Systems　51.2　Stochastic and Deterministic Dynamic Mathematical Models　71.2.1　Stationary and Nonstationary Stochastic Models for Forecasting and Control　71.2.2　Transfer Function Models　121.2.3　Models for Discrete Control Systems　141.3　Basic Ideas in Model Building　161.3.1　Parsimony　161.3.2　Iterative Stages in the Selection of a Model　16Part I　Stochastic Models and Their Forecasting　192　AUTOCORRELATION FUNCTION AND SPECTRUM OF STATIONARY PROCESSES　212.1　Autocorrelation Properties of Stationary Models　212.1.1　Time Series and Stochastic Processes　212.1.2　Stationary Stochastic Processes　232.1.3　Positive Definiteness and the Autocovariance Matrix　262.1.4　Autocovariance and Autocorrelation Functions　292.1.5　Estimation of Autocovariance and Autocorrelation Functions　302.1.6　Standard Error of Autocorrelation Estimates　322.2　Spectral Properties of Stationary Models　352.2.1　Periodogram of a Time Series　352.2.2　Analysis of Variance　362.2.3　Spectrum and Spectral Density Function　372.2.4　Simple Examples of Autocorrelation and Spectral Density Functions　412.2.5　Advantages and Disadvantages of the Autocorrelation and Spectral Density Functions　43A2.1　Link Between the Sample Spectrum and Autocovariance Function Estimate　443　LINEAR STATIONARY MODELS　463.1　General Linear Process　463.1.1　Two Equivalent Forms for the Linear Process　463.1.2　Autocovariance Generating Function of a Linear Process　493.1.3　Stationarity and Invertibility Conditions for a Linear Process　503.1.4　Autoregressive and Moving Average Processes　523.2　Autoregressive Processes　543.2.1　Stationarity Conditions for Autoregressive Processes　543.2.2　Autocorrelation Function and Spectrum of Autoregressiue Processes　55　3.2.3　First-Order Autoregressive (Markov) Process　583.2.4　Second-Order Autoregressive Process　603.2.5　Partial Autocorrelation Function　643.2.6　Estimation of the Partial Autocorrelation Function　673.2.7　Standard Errors of Partial Autocorrelation Estimates　683.3　Moving Average Processes　693.3.1　Invertibility Conditions for Moving Average Processes　693.3.2　Autocorrelation Function and Spectrum of Moving Average Processes　703.3.3　First-Order Moving Average Process　723.3.4　Second-Order Moving Average Process　733.3.5　Duality Between Autoregressive and Moving Average Processes　753.4　Mixed Autoregressive-Moving Average Processes　773.4.1　Stationarity and Invertibility Properties　773.4.2　Autocorrelation Function and Spectrum of Mixed Processes　783.4.3　First-Order Autoregressive-First-Order Moving Average Process　803.4.4　Summary　83A3.1　Autocovariances Autocovariance Generating Function and Stationarity Conditions for a General Linear Process　85A3.2　Recursive Method for Calculating Estimates of Autoregressive Parameters　874　LINEAR NONSTATIONARY MODELS　894.1　Autoregressive Integrated Moving Average Processes　894.1.1　Nonstationary First-Order Autoregressive Process　894.1.2　General Model for a Nonstationary Process Exhibiting Homogeneity　924.1.3　General Form of the Autoregressive Integrated Moving Average Process　964.2　Three Explicit Forms for the Autoregressive Integrated Moving Average Model　994.2.1　Difference Equation Form of the Model　994.2.2　Random Shock Form of the Model　I004.2.3　Inverted Form of the Model　1064.3　Integrated Moving Average Processes　1094.3.1　Integrated Moving Average Process of Order (0,1,1)　1104.3.2　Integrated Moving Average Process of Order (0,2,2)　1144.3.3　General Integrated Moving Average Process of Order (0,d,q)　118A4.1　Linear Difference Equations　120A4.2　IMA(0,1,1) Process With Deterministic Drift　125A4.3　ARIMA Processes With Added Noise　126A4.3.1　Sum of Two Independent Moving Average Processes　126A4.3.2　Effect of Added Noise on the General Model　127A4.3.3　Example for an IMA(O,1,1) Process with Added White Noise　128A4.3.4　Relation Between the IMA(O,1,1) Process and a Random Walk　129A4.3.5　Autocovariance Function of the General Model with Added Correlated Noise　1295　FORECASTING　1315.1　Minimum Mean Square Error Forecasts and Their Properties　1315.1.1　Derivation of the Minimum Mean Square Error Forecasts　1335.1.2　Three Basic Forms for the Forecast　1355.2　Calculating and Updating Forecasts　1395.2.1　Convenient Format for the Forecasts　1395.2.2　Calculation of the ψ Weights　1395.2.3　Use of the ψ Weights in Updating the Forecasts　1415.2.4　Calculation of the Probability Limits of the Forecasts at Any Lead Time　1425.3　Forecast Function and Forecast Weights　1455.3.1　Eventual Forecast Function Determined by the Autoregressive Operator　1465.3.2　Role of the Mooing Average Operator in Fixing the Initial Values　1475.3.3　Lead l Forecast Weights　1485.4　Examples of Forecast Functions and Their Updating　1515.4.1　Forecasting an IMA(O,1,1) Process　1515.4.2　Forecasting an IMA(O,2,2) Process　1545.4.3　Forecasting a General IMA(O,d,q) Process　1565.4.4　Forecasting Autoregressive Processes　1575.4.5　Forecasting a (1,O,1) Process　1605.4.6　Forecasting a (1,1,1) Process　1625.5　Use of State Space Model Formulation for Exact Forecasting　1635.5.1　State Space Model Representation for the ARIMA Process　1635.5.2　Kalman Filtering Relations for Use in Prediction　1645.6　Summary　166A5.1　Correlations Between Forecast Errors　169A5.1.1　Autocorrelation Function of Forecast Errors at Different Origins　169A5.1.2　Correlation Between Forecast Errors at the Same Origin with Different Lead Times　170A5.2　Forecast Weights for Any Lead Time　172A5.3　Forecasting in Terms of the General Integrated Form　174A5.3.1　General Method of Obtaining the Integrated Form　174A5.3.2　Updating the General Integrated Form　176A5.3.3　Comparison with the Discounted Least Squares Method　176Part II　Stochastic Model Building　1816　MODELDENTIFICATION　1836.l　Objectives of Identification　1836.1.1　Stages in the Identification Procedure　1846.2　Identification Techniques　1846.2.1　Use of the Autocorrelation and Partial Autocorrelation Functions in Identification　1846.2.2　Standard Errors for Estimated Autocorrelations and Partial Autocorrelations　1886.2.3　Identification of Some Actual Time Series　1886.2.4　Some Additional Model Identification Tools　1976.3　Initial Estimates for the Parameters　2026.3.1　Uniqueness of Estimates Obtained from the Autocovariance Function　2026.3.2　Initial Estimates for Moving Average Processes　2026.3.3　Initial Estimates for Autoregressive Processes　2046.3.4　Initial Estimates for Mixed Autoregressive-Moving Average Processes　2066.3.5　Choice Between Stationary and Nonstationary Models in Doubtful Cases　2076.3.6　More Formal Tests for Unit Roots in ARIMA Models　2086.3.7　Initial Estimate of Residual Variance　2116.3.8　Approximate Standard Error for 　2126.4　Model Multiplicity　2146.4.1　Multiplicity of Autoregressive-Moving Average Models　2146.4.2　Multiple Moment Solutions for Moving Average Parameters　2166.4.3　Use of the Backward Process to Determine Starting Values　218A6.1　Expected Behavior of the Estimated Autocorrelation Function for a Nonstationary Process　218A6.2　General Method for Obtaining Initial Estimates of the Parameters of a Mixed Autoregressive-Moving Average Process　2207　MODELESTIMATION　2247.l　Study of the Likelihood and Sum of Squares Functions　2247.1.1　Likelihood Function　2247.1.2　Conditional Likelihood for an ARIMA Process　2267.1.3　Choice of Starting Values for Conditional Calculation　2277.1.4　Unconditional Likelihood; Sum of Squares Function; Least Squares Estimates　2287.1.5　General Procedure for Calculating the Unconditional Sum of Squares　2337.1.6　Graphical Study of the Sum of Squares Function　2387.1.7　Description of“Well-Behaved” Estimation Situations; Confidence Regions　2417.2　Nonlinear Estimation　2487.2.1　General Method of Approach　2487.2.2　Numerical Estimates of the Derivatives　2497.2.3　Direct Evaluation of the Derivatives　2517.2.4　General Least Squares Algorithm for the Conditional Model　2527.2.5　Summary of Models Fitted to Series A to F　2557.2.6　Large-Sample Information Matrices and Covariance Estimates　2567.3　Some Estimation Results for Specific Models　2597.3.1　Autoregressive Processes　2607.3.2　Moving Average Processes　2627.3.3　Mixed Processes　2627.3.4　Separation of Linear and Nonlinear Components in Estimation　2637.3.5　Parameter Redundancy　2647.4　Estimation Using Bayes' Theorem　2677.4.1　Bayes' Theorem　2677.4.2　Bayesian Estimation of Parameters　2697.4.3　Autoregressive Processes　2707.4.4　Moving Average Processes　2727.4.5　Mixed processes　2747.5　Likelihood Function Based on The State Space Model　275A7.1　Review of Normal Distribution Theory　279A7.1.1　Partitioning of a Positive-Definite Quadratic Form　279A7.1.2　Two Useful Integrals　280A7.1.3　Normal Distribution　281A7.1.4　Student's t-Distribution　283A7.2　Review of Linear Least Squares Theory　286A7.2.1　Normal Equations　286A7.2.2　Estimation of Residual Variance　287A7.2.3　Covariance Matrix of Estimates　288A7.2.4　Confidence Regions　288A7.2.5　Correlated Errors　288A7.3　Exact Likelihood Function for Moving Average and Mixed Processes　289A7.4　Exact Likelihood Function for an Autoregressive Process　296A7.5　Examples of the Effect of Parameter Estimation Errors on Probability Limits for Forecasts　304A7.6　Special Note on Estimation of Moving Average Parameters　3078　MODEL DIAGNOSTIC CHECKING　3088.1　Checking the Stochastic Model　3088.1.1　General Philosophy　3088.1.2　Overfitting　3098.2　Diagnostic Checks Applied to Residuals　3128.2.1　Autocorrelation Check　3128.2.2　Portmanteau Lack-of-Fit Test　3148.2.3　Model Inadequacy Arising from Changes in Parameter Values　3178.2.4　Score Tests for Model Checking　3188.2.5　Cumulative Periodogram Check　3218.3　Use of Residuals to Modify the Model　3248.3.1　Nature of the Correlations in the Residuals When an Incorrect Model Is Used　3248.3.2　Use of Residuals to Modify the Model　3259　SEASONALMODELS　3279.1　Parsimonious Models for Seasonal Time Series　3279.1.1　Fitting versus Forecasting　3289.1.2　Seasonal Models Involving Adaptive Sines and Cosines　3299.1.3　General Multiplicative Seasonal Model　3309.2　Representation of the Airline Data by a Multiplicative (0,1,1) ~ (0,1,1)12 Seasonal Model　3339.2.1　Multiplicative (0,l,l) ~ (0,l,1)12 Model　3339.2.2　Forecasting　3349.2.3　Identification　3419.2.4　Estimation　3449.2.5　Diagnostic Checking　3499.3　Some Aspects of More General Seasonal Models　3519.3.1　Multiplicative and Nonmultiplicative Models　3519.3.2　Identification　3539.3.3　Estimation　3559.3.4　Eventual Forecast Functions for Various Seasonal Models　3559.3.5　Choice of Transformation　3589.4　Structural Component Models and Deterministic Seasonal Components　3599.4.1　Deterministic Seasonal and Trend Components and Common Factors　3609.4.2　Models with Regression Terms and Time Series Error Terms　361A9.1　Autocovariances for Some Seasonal Models　366Part III　Transfer Function Model Building　37110　TRANSFER FUNCTION MODELS　37310.1　Linear Transfer Function Models　37310.1.1　Discrete Transfer Function　37410.1.2　Continuous Dynamic Models Represented by Differential Equations　37610.2　Discrete Dynamic Models Represented by Difference Equations　38110.2.1　General Form of the Difference Equation　38110.2.2　Nature of the Transfer Function　38310.2.3　First- and Second-Order Discrete Transfer Function Models　38410.2.4　Recursive Computation of Output for Any Input　39010.2.5　Transfer Function Models with Added Noise　39210.3　Relation Between Discrete and Continuous Models　39210.3.1　Response to a Pulsed Input　39310.3.2　Relationships for First-and Second-Order Coincident Systems　39510.3.3　Approximating General Continuous Models by Discrete Models　398A10.1　Continuous Models With Pulsed Inputs　399A10.2　Nonlinear Transfer Functions and Linearization　40411　IDENTIFICATION FITTING AND CHECKING OF TRANSFER FUNCTION MODELS　407ll.1　Cross Correlation Function　40811.1.1　Properties of the Cross Covariance and Cross Correlation Functions　40811.1.2　Estimation of the Cross Covariance and Cross Correlation Functions　41111.1.3　Approximate Standard Errors of Cross Correlation Estimates　41311.2　Identification of Transfer Function Models　41511.2.1　Identification of Transfer Function Models by Prewhitening the Input　41711.2.2　Example of the Identification of a Transfer Function Model　41911.2.3　Identification of the Noise Model　42211.2.4　Some General Considerations in Identifying Transfer Function Models　42411.3　Fitting and Checking Transfer Function Models　42611.3.1　Conditional Sum of Squares Function　42611.3.2　Nonlinear Estimation　42911.3.3　Use of Residuals for Diagnostic Checking　43111.3.4　Specific Checks Applied to the Residuals　43211.4　Some Examples of Fitting and Checking Transfer Function Models　43511.4.1　Fitting and Checking of the Gas Furnace Model　43511.4.2　Simulated Example with Two Inputs　44111.5　Forecasting Using Leading Indicators　44411.5.1　Minimum Mean Square Error Forecast　44411.5.2　Forecast of C02 Output from Gas Furnace　44811.5.3　Forecast of Nonstationary Sales Data Using a Leading Indicator　45111.6　Some Aspects of the Design of Experiments to Estimate Transfer Functions　453A11.1　Use of Cross Spectral Analysis for Transfer Function Model Identification　455All.I.1　Identification of Single Input Transfer Function Models　455All.l.2　Identification of Multiple Input Transfer Function Models　456AI1.2　Choice of Input to Provide Optimal Parameter Estimates　457All.2.1　Design of Optimal Inputs for a Simple System　457All.2.2　Numerical Example　46012　INTERVENTION ANALYSIS MODELS AND OUTLIER DETECTION　46212.1　Intervention Analysis Methods　46212.1.1　Models for Intervention Analysis　46212.1.2　Example of Intervention Analysis　46512.1.3　Nature of the MLE for a Simple Level Change Parameter Model　46612.2　Outlier Analysis for Time Series　46912.2.1　Models for Additive and Innovational Outliers　46912.2.2　Estir m ation of Outlier Effect for Known Timing of the Outlier　47012.2.3　Iterative Procedure for Outlier Detection　47112.2.4　Examples of Analysis of Outliers　47312.3　Estimation for ARMA Models With Missing Values　474Part IV　Design of Discrete Control Schemes　48113　ASPECTS OF PROCESS CONTROL　48313.1　Process Monitoring and Process Adjustment　48413.1.1　Process Monitoring　48413.1.2　Process Adjustment　48713.2　Process Adjustment Using Feedback Control~48813.2.1　Feedback Adjustment Chart　48913.2.2　Modeling the Feedback Loop　49213.2.3　Simple Models for Disturbances and Dynamics　49313.2.4　General Minimum Mean Square Error Feedback Control Schemes　49713.2.5　Manual Adjustment for Discrete Proportional-Integral Schemes　49913.2.6　Complementary Roles of Monitoring and Adjustment　50313.3　Excessive Adjustment Sometimes Required by MMSE Control　50513.3.1　Constrained Control　50613.4　Minimum Cost Control With Fixed Costs of Adjustment And Monitoring　50813.4.1　Bounded Adjustment Scheme for Fixed Adjustment Cost　50813.4.2　Indirect Approach for Obtaining a Bounded Adjustment Scheme　51013.4.3　Inclusion of the Cost of Monitoring　51113.5　Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes　514A13.1　Feedback Control Schemes Where the Adjustment Variance Is Restricted　516A13.1.1　Derivation of Optimal Adjustment　517A13.2　Choice of the Sampling Interval　526A13.2.1　Illustration of the Effect of Reducing Sampling Frequency　526A13.2.2　Sampling an IMA(O,I,I) Process　526Part V　Charts and Tables　531COLLECTION OF TABLES AND CHARTS　533COLLECTION OF TIME SERIES USED FOR EXAMPLES IN THE TEXT AND IN EXERCISES　540REFERENCES　556Part VI　EXERCISES AND PROBLEMS　569INDEX　589

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　　時間序列分析是一門實用性很強、蓬勃發(fā)展的數(shù)據(jù)分析技術(shù)，現(xiàn)在廣泛地應用于工業(yè)質(zhì)量控制、生物基因工程和金融數(shù)據(jù)分析等諸多領(lǐng)域。而這一切的發(fā)展不能不提到G.E.P.BOX和G.M.JE-NKINS以及二人合著的最早于1970年出版的《時間序列分析——預測與控制》。由于二位對時間序列數(shù)據(jù)分析的巨大貢獻，大家將本書提出的ARIMA模型命名為BOX-JENKINS模型。　　在這本時間序列分析經(jīng)典之作中，幾位統(tǒng)計大家用極其通俗的語言，運用大量的實例，深入淺出而又形象地闡明時間序列分析的精髓，使讀者免去過多繁雜的數(shù)學公式推導證明，而很快掌握實踐的技巧，體會其中直觀而深刻的思想。相信每一位研讀此書的讀者都會獲益匪淺。

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