Chatfield C. The Analysis of Time Series: An Introduction

5th edition. — Chapman & Hall, 1996. — 304 p.A textbook for graduate and undergraduate students taking courses in time series. Topics include probability models, Box-Jenkins forecasting, spectral analysis, linear systems, and system identification.Preface to fifth edition.
Abbreviations and notation.
Introduction.
Some representative time series.
Terminology.
Objectives of time-series analysis.
Approaches to time-series analysis.
Review of books on time series.
Simple descriptive techniques.
Types of variation.
Stationary time series.
The time plot.
Transformations.
Analysing series which contain a trend.
Analysing series which contain seasonal variation.
Autocorrelation.
Other tests of randomness.
Probability models for time series.
Stochastic processes.
Stationary processes.
The autocorrelation function.
Some useful stochastic processes.
The World decomposition theorem.
Estimation in the time domain.
Estimation the autocovariance and autocorrelation functions.
Fitting an autoregressive process.
Fitting a moving average process.
Estimating the parameters of an ARMA model.
Estimating the parameters of an ARIMA model.
The Box-Jenkins seasonal (SARIMA) model.
Residual analysis.
General remarks on model building.
Forecasting.
Introduction.
Univariate procedures.
Multivariate procedures.
A comparative review of forecasting procedures.
Some examples.
Prediction theory.
Stationary processes in the frequency domain.
Introduction.
The spectral distribution function.
The spectral density function.
The spectrum of a continuous process.
Derivation of selected spectra.
Spectral analysis.
Fourier analysis.
A simple sinusoidal model.
Periodogram analysis.
Spectral analysis: some consistent estimation procedures.
Confidence intervals for the spectrum.
A comparison of different estimation procedures.
Analysing a continuous time series.
Discussion.
Bivariate processes.
Cross-covariance and cross-correlation functions.
The cross-spectrum.
Linear systems.
Introduction.
Linear systems in the time domain.
Linear systems in the frequency domain.
Identification of linear systems.
State-space models and the Kalman filter.
State-space models.
The Kalman filter.
Non-linear models.
Introduction.
Some models with non-linear structure.
Models for changing variance.
Neural networks.
Chaos.
Concluding remarks.
Multivariate time-series modelling.
Introduction.
Single equation models.
Vector autoregressive models.
Vector ARMA models.
Fitting VAR and VARMA models.
Co-integration.
Some other topics.
Model identification tools.
Modelling non-stationary series.
The effect of model uncertainty.
Control theory.
Miscellanea.
Appendix.
The Fourier, Laplace and Z transforms.
The Dirac delta function.
Covariance.
Some worked examples.
References.
Answers to exercises.
Author index.
Subject index.