The analysis of Time Series an Introduction

Contents
Preface to the Sixth Edition xi
Abbreviations and Notation xiii
1 Introduction 1
1.1 Some Representative Time Series 1
1.2 Terminology 5
1.3 Objectives of Time-Series Analysis 6
1.4 Approaches to Time-Series Analysis 8
1.5 Review of Books on Time Series 8
2 Simple Descriptive Techniques 11
2.1 Types of Variation 11
2.2 Stationary Time Series 13
2.3 The Time Plot 13
2.4 Transformations 14
2.5 Analysing Series that Contain a Trend 15
2.6 Analysing Series that Contain Seasonal Variation 20
2.7 Autocorrelation and the Correlogram 22
2.8 Other Tests of Randomness 28
2.9 Handling Real Data 29
3 Some Time-Series Models 33
3.1 Stochastic Processes and Their Properties 33
3.2 Stationary Processes 34
3.3 Some Properties of the Autocorrelation Function 36
3.4 Some Useful Models 37
3.5 The Wold Decomposition Theorem 50
4 Fitting Time-Series Models in the Time Domain 55
4.1 Estimating Autocovariance and Autocorrelation Functions 55
4.2 Fitting an Autoregressive Process 59
4.3 Fitting a Moving Average Process 62
4.4 Estimating Parameters of an ARMA Model 64
4.5 Estimating Parameters of an ARIMA Model 65
4.6 Box-Jenkins Seasonal ARIMA Models 66
4.7 Residual Analysis 67
4.8 General Remarks on Model Building 70
5 Forecasting 73
5.1 Introduction 73
5.2 Univariate Procedures 75
5.3 Multivariate Procedures 87
5.4 Comparative Review of Forecasting Procedures 90
5.5 Some Examples 98
5.6 Prediction Theory 103
6 Stationary Processes in the Frequency Domain 107
6.1 Introduction 107
6.2 The Spectral Distribution Function 107
6.3 The Spectral Density Function 111
6.4 The Spectrum of a Continuous Process 113
6.5 Derivation of Selected Spectra 114
7 Spectral Analysis 121
7.1 Fourier Analysis 121
7.2 A Simple Sinusoidal Model 122
7.3 Periodogram Analysis 126
7.4 Some Consistent Estimation Procedures 130
7.5 Confidence Intervals for the Spectrum 139
7.6 Comparison of Different Estimation Procedures 140
7.7 Analysing a Continuous Time Series 144
7.8 Examples and Discussion 146
8 Bivariate processes 155
8.1 Cross-Covariance and Cross-Correlation 155
8.2 The Cross-Spectrum 159
9 Linear Systems 169
9.1 Introduction 169
9.2 Linear Systems in the Time Domain 171
9.3 Linear Systems in the Frequency Domain 175
9.4 Identification of Linear Systems 190
10 State-Space Models and the Kalman Filter 203
10.1 State-Space Models 203
10.2 The Kalman Filter 211
11 Non-Linear Models 217
11.1 Introduction 217
11.2 Some Models with Non-Linear Structure 222
11.3 Models for Changing Variance 227
11.4 Neural Networks 230
11.5 Chaos 235
11.6 Concluding Remarks 238
11.7 Bibliography 240
12 Multivariate Time-Series Modelling 241
12.1 Introduction 241
12.2 Single Equation Models 245
12.3 Vector Autoregressive Models 246
12.4 Vector ARMA Models 249
12.5 Fitting VAR and VARMA Models 250
12.6 Co-integration 252
12.7 Bibliography 253
13 Some More Advanced Topics 255
13.1 Model Identification Tools 255
13.2 Modelling Non-Stationary Series 257
13.3 Fractional Differencing and Long-Memory Models 260
13.4 Testing for Unit Roots 262
13.5 Model Uncertainty 264
13.6 Control Theory 266
13.7 Miscellanea 268
14 Examples and Practical Advice 277
14.1 General Comments 277
14.2 Computer Software 278
14.3 Examples 280
14.4 More on the Time Plot 290
14.5 Concluding Remarks 292
14.6 Data Sources and Exercises 292
A Fourier, Laplace and z-Transforms 295
B Dirac Delta Function 299
C Covariance and Correlation 301
D Some MINITAB and S-PLUS Commands 303
Answers to Exercises 307
References 315
Index 329

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