This new edition of this classic title, now in its seventh edition, presents a balanced and comprehensive introduction to the theory, implementation, and practice of time series analysis. The book covers a wide range of topics, including ARIMA models, forecasting methods, spectral analysis, linear systems, state-space models, the Kalman filters, nonlinear models, volatility models, and multivariate models. It also presents many examples and implementations of time series models and methods to reflect advances in the field.
Highlights of the seventh edition:
- — A new chapter on univariate volatility models
- — A revised chapter on linear time series models
- — A new section on multivariate volatility models
- — A new section on regime switching models
- — Many new worked examples, with R code integrated into the text
The book can be used as a textbook for an undergraduate or a graduate level time series course in statistics. The book does not assume many prerequisites in probability and statistics, so it is also intended for students and data analysts in engineering, economics, and finance.
Author(s): Chris Chatfield; Haipeng Xing
Series: Chapman & Hall/CRC texts in statistical science series
Edition: 7 ed.
Publisher: CRC Press
Year: 2019
Language: English
Commentary: New edition. Added bookmarks to exercise.
Pages: 398
Preface to the Seventh Edition
Abbreviations and Notation
1 Introduction
1.1 Some Representative Time Series
1.2 Terminology
1.3 Objectives of Time Series Analysis
1.4 Approaches to Time Series Analysis
1.5 Review of Books on Time Series
2 Basic Descriptive Techniques
2.1 Types of Variation
2.2 Stationary Time Series
2.3 The Time Plot
2.4 Transformations
2.5 Analysing Series that Contain a Trend and No Seasonal Variation
2.5.1 Curve Fitting
2.5.2 Filtering
2.5.3 Differencing
2.5.4 Other approaches
2.6 Analysing Series that Contain a Trend and Seasonal Variation
2.7 Autocorrelation and the Correlogram
2.7.1 The correlogram
2.7.2 Interpreting the correlogram
2.8 Other Tests of Randomness
2.9 Handling Real Data
3 Some Linear Time Series Models
3.1 Stochastic Processes and Their Properties
3.2 Stationary Processes
3.3 Properties of the Autocorrelation Function
3.4 Purely Random Processes
3.5 Random Walks
3.6 Moving Average Processes
3.6.1 Stationarity and autocorrelation function of an MA process
3.6.2 Invertibility of an MA process
3.7 Autoregressive Processes
3.7.1 First-order process
3.7.2 General-order process
3.8 Mixed ARMA Models
3.8.1 Stationarity and invertibility conditions
3.8.2 Yule-Walker equations and autocorrelations
3.8.3 AR and MA representations
3.9 Integrated ARMA (or ARIMA) Models
3.10 Fractional Differencing and Long-Memory Models
3.11 The General Linear Process
3.12 Continuous Processes
3.13 The Wold Decomposition Theorem
4 Fitting Time Series Models in the Time Domain
4.1 Estimating Autocovariance and Autocorrelation Functions
4.1.1 Using the correlogram in modelling
4.1.2 Estimating the mean
4.1.3 Ergodicity
4.2 Fitting an Autoregressive Process
4.2.1 Estimating parameters of an AR process
4.2.2 Determining the order of an AR process
4.3 Fitting a Moving Average Process
4.3.1 Estimating parameters of an MA process
4.3.2 Determining the order of an MA process
4.4 Estimating Parameters of an ARMA Model
4.5 Model Identification Tools
4.6 Testing for Unit Roots
4.7 Estimating Parameters of an ARIMA Model
4.8 Box{Jenkins Seasonal ARIMA Models
4.9 Residual Analysis
4.10 General Remarks on Model Building
5 Forecasting
5.1 Introduction
5.2 Extrapolation and Exponential Smoothing
5.2.1 Extrapolation of trend curves
5.2.2 Simple exponential smoothing
5.2.3 The Holt and Holt{Winters forecasting procedures
5.3 The Box{Jenkins Methodology
5.3.1 The Box-Jenkins procedures
5.3.2 Other methods
5.3.3 Prediction intervals
5.4 Multivariate Procedures
5.4.1 Multiple regression
5.4.2 Econometric models
5.4.3 Other multivariate models
5.5 Comparative Review of Forecasting Procedures
5.5.1 Forecasting competitions
5.5.2 Choosing a non-automatic method
5.5.3 A strategy for non-automatic univariate forecasting
5.5.4 Summary
5.6 Prediction Theory
6 Stationary Processes in the Frequency Domain
6.1 Introduction
6.2 The Spectral Distribution Function
6.3 The Spectral Density Function
6.4 The Spectrum of a Continuous Process
6.5 Derivation of Selected Spectra
7 Spectral Analysis
7.1 Fourier Analysis
7.2 A Simple Sinusoidal Model
7.3 Periodogram Analysis
7.3.1 The relationship between the periodogram and the autocovariance function
7.3.2 Properties of the periodogram
7.4 Some Consistent Estimation Procedures
7.4.1 Transforming the truncated autocovariance function
7.4.2 Hanning
7.4.3 Hamming
7.4.4 Smoothing the periodogram
7.4.5 The fast Fourier transform (FFT)
7.5 Confidence Intervals for the Spectrum
7.6 Comparison of Different Estimation Procedures
7.7 Analysing a Continuous Time Series
7.8 Examples and Discussion
8 Bivariate Processes
8.1 Cross-Covariance and Cross-Correlation
8.1.1 Examples
8.1.2 Estimation
8.1.3 Interpretation
8.2 The Cross-Spectrum
8.2.1 Examples
8.2.2 Estimation
8.2.3 Interpretation
9 Linear Systems
9.1 Introduction
9.2 Linear Systems in the Time Domain
9.2.1 Some types of linear systems
9.2.2 The impulse response function: An explanation
9.2.3 The step response function
9.3 Linear Systems in the Frequency Domain
9.3.1 The frequency response function
9.3.2 Gain and phase diagrams
9.3.3 Some examples
9.3.4 General relation between input and output
9.3.5 Linear systems in series
9.3.6 Design of Filters
9.4 Identification of Linear Systems
9.4.1 Estimating the frequency response function
9.4.2 The Box{Jenkins approach
9.4.3 Systems involving feedback
10 State-Space Models and the Kalman Filter
10.1 State-Space Models
10.1.1 The random walk plus noise model
10.1.2 The linear growth model
10.1.3 The basic structural model
10.1.4 State-space representation of an AR(2) process
10.1.5 Bayesian forecasting
10.1.6 A regression model with time-varying coefficients
10.1.7 Model building
10.2 The Kalman Filter
11 Non-Linear Models
11.1 Introduction
11.1.1 Why non-linearity?
11.1.2 What is a linear model?
11.1.3 What is a non-linear model?
11.1.4 What is white noise?
11.2 Non-Linear Autoregressive Processes
11.3 Threshold Autoregressive Models
11.4 Smooth Transition Autoregressive Models
11.5 Bilinear Models
11.6 Regime-Switching Models
11.7 Neural Networks
11.8 Chaos
11.9 Concluding Remarks
11.10 Bibliography
12 Volatility Models
12.1 Structure of a Model for Asset Returns
12.2 Historic Volatility
12.3 Autoregressive Conditional Heteroskedastic (ARCH) Models
12.4 Generalized ARCH Models
12.5 The ARMA-GARCH Models
12.6 Other ARCH-Type Models
12.6.1 The integrated GARCH model
12.6.2 The exponential GARCH model
12.7 Stochastic Volatility Models
12.8 Bibliography
13 Multivariate Time Series Modelling
13.1 Introduction
13.1.1 One equation or many?
13.1.2 The cross-correlation function
13.1.3 Initial data analysis
13.2 Single Equation Models
13.3 Vector Autoregressive Models
13.3.1 VAR(1) models
13.3.2 VAR(p) models
13.4 Vector ARMA Models
13.5 Fitting VAR and VARMA Models
13.6 Co-Integration
13.7 Multivariate Volatility Models
13.7.1 Exponentially weighted estimate
13.7.2 BEKK models
13.8 Bibliography
14 Some More Advanced Topics
14.1 Modelling Non-Stationary Time Series
14.2 Model Uncertainty
14.3 Control Theory
14.4 Miscellanea
14.4.1 Autoregressive spectrum estimation
14.4.2 Wavelets
14.4.3 `Crossing' problems
14.4.4 Observations at unequal intervals, including missing
values
14.4.5 Outliers and robust methods
14.4.6 Repeated measurements
14.4.7 Aggregation of time series
14.4.8 Spatial and spatio-temporal series
14.4.9 Time series in Finance
14.4.10 Discrete-valued time series
Appendix A Fourier, Laplace, and z-Transforms
Appendix B Dirac Delta Function
Appendix C Covariance and Correlation
Answers to Exercises
References
Index
