The analysis of time series: an introduction

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