The Analysis of Time Series6th edition

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