The Analysis of Time Series

INTRODUCTION
Some Representative Time Series
Terminology
Objectives of Time-Series Analysis
Approaches to Time-Series Analysis
Review of Books of Time Series
SIMPLE DESCRIPTIVE TECHNIQUES
Types of Variation
Stationary Time Series
The Time Plot
Transformation
Analysing Series that Contain a Trend
Analysing Series that Contain Seasonal Variation
Autocorrelation and the Correlogram
Other Tests of Randomness
Handling Real Data
PROBABILITY MODELS FOR TIME SERIES
Stochastic Processes and their Properties
Stationary Processes
Some Properties of the Autocorrelation Function
Some Useful Models
The Wold Decomposition Theorem
FITTING TIME-SERIES MODELS (IN THE TIME DOMAIN)
Estimating 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
Examples and Discussion
BIVARIATE PROCESSES
The 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 Nonlinear Structure
Models for Changing Variance
Neural Networks
Chaos
Concluding Remarks
Bibliography
MULTIVARIATE TIME-SERIES MODELLING
Introduction
Single Equation Models
Vector Autoregressive Models
Vector ARMA Models
Fitting VAR and VARMA Models
Co-integration
Bibliography
SOME MORE ADVANCED TOPICS
Model Identification Tools
Modelling Non-Stationary Series
Fractional Differencing and Long-Memory Models
Testing for Unit Roots
The Effect of Model Uncertainty
Control Theory
Miscellanea
EXAMPLES AND PRACTICAL ADVICE
General Comments
Computer Software
Examples
More on the Time Plot
Concluding Remarks
Data Sources and Exercises
APPENDICES
The Fourier, Laplace, and z-Transforms
The Dirac Delta Function
Covariance and Correlation
Some MINITAB and S-PLUS Commands
ANSWERS TO EXERCISES
REFERENCES