The Analysis of Time Series: An Introduction
| Publisher | Chapman & Hall, Limited, CRC Press |
| Format | Paperback |
| Language | English |
| This Edition Published | 1996-04-01 |
| Pages / Font | 304 pages |
| ISBN | 0412716402 |
| Chapters | 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 |
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