«As an introduction to techniques for analyzing discrete time series, this textbook explains probability models, the spectral density function, time-invariant linear systems, state-space models, nonlinear models, and multivariate time series models.» — «Book News, Inc.»
Author(s): Chris Chatfield
Edition: 5 ed.
Publisher: Chapman and Hall/CRC
Year: 1996
Language: English
Pages: 304
Preface to fifth 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 Simple descriptive techniques
2.1 Types of variation
2.2 Stationary time scries
2.3 The time plot
2.4 Transformations
2.5 Analysing scries which contain a trend
2.6 Analysing series which contain seasonal variation
2.7 Autocorrelation
2.8 Other tests of randomness
Exercises
3 Probability models for time series
3.1 Stochastic processes
3.2 Stationary processes
3.3 The autocorrelation function
3.4 Some useful stochastic processes
3.5 The Wold decomposition theorem
Exercises
4 Estimation in the time domain
4.1 Estimating the autocovariance and autocorrelation functions
4.2 Fitting an autoregressive process
4.3 Fitting a moving average process
4.4 Estimating the parameters of an ARMA model
4.5 Estimating the parameters of an ARIMA model
4.6 The Box-Jenkins seasonal (SARIMA) model
4.7 Residual analysis
4.8 General remarks on model building
Exercises
5 Forecasting
5.1 Introduction
5.2 Univariate procedures
5.3 Multivariate procedures
5.4 A comparative review of forecasting procedures
5.5 Some examples
5.6 Prediction theory
Exercises
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 Exercises
7 Spectral analysts
7.1 Fourier analysis
7.2 A simple sinusoidal model
7.3 Periodogram analysis
7.4 Spectral analysis: some consistent estimation procedures
7.5 Confidence intervals for the spectrum
7.6 A comparison of different estimation procedures
7.7 Analysing a continuous time series
7.8 Discussion
Exercises
8 Bivariate processes
8.1 Cross-covariance and cross-correlation functions
8.2 The cross-spectrum
Exercises
9 Linear systems
9.1 Introduction
9.2 Linear systems in the time domain
9.3 Linear systems in the frequency domain
9.4 Identification of linear systems
Exercises
10 Slate-space models and the Kalman filter
10.1 State-space models
10.2 The Kalman filter
Exercises
11 Non-linear models
11.1 Introduction
11.2 Some models with non-linear structure
11.3 Models for changing variance
11.4 Neural networks
11.5 Chaos
11.6 Concluding remarks
12 Multivariate time-series modelling
12.1 Introduction
12.2 Single equation models
12.3 Vector autoregressive models
12.4 Vector ARMA models
12.5 Fitting VAR and VARMA models
12.6 Co-integration
13 Some other topics
13.1 Model identification tools
13.2 Modelling non-stationary series
13.3 The effect of model uncertainty
13.4 Control theory
13.5 Miscellanea
Appendix A The Fourier, Laplace and Z transforms
Appendix В The Dirac delta function
Appendix C Covariance
Appendix D Some worked examples
References
Answers to exercises
Author index
Subject index
