The analysis of time series : an introduction / Chris Chatfield.

Includes bibliographical references (p. 315-327) and index.

1.1 Some Representative Time Series 1 -- 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 -- 5.2 Univariate Procedures 75 -- 5.3 Multivariate Procedures 87 -- 5.4 Comparative Review of Forecasting Procedures 90 -- 5.6 Prediction Theory 103 -- 6 Stationary Processes in the Frequency Domain 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 -- 8 Bivariate processes 155 -- 8.1 Cross-Covariance and Cross-Correlation 155 -- 8.2 The Cross-Spectrum 159 -- 9 Linear Systems 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 -- 11.2 Some Models with Non-Linear Structure 222 -- 11.3 Models for Changing Variance 227 -- 11.4 Neural Networks 230 -- 11.5 Chaos 235 -- 12 Multivariate Time-Series Modelling 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 -- 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 -- 14.2 Computer Software 278 -- 14.4 More on the Time Plot 290 -- 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

"Since 1975, The Analysis of Time Series: An Introduction has introduced legions of statistics students and researchers to the theory and practice of time series analysis. The sixth edition provides an accessible, comprehensive introduction to the theory and practice of time series analysis. The treatment covers a wide range of topics, including ARIMA probability models, forecasting methods, spectral analysis, linear systems, state-space models, and the Kalman filter. It also addresses nonlinear, multivariate, and long-memory models. The author has carefully updated each chapter, added new discussions, incorporated new datasets, and made those datasets available at www.crcpress.com."--BOOK JACKET