The goals of this book are to develop an appreciation for the richness and versatility of modern time series analysis as a tool for analyzing data, and still maintain a commitment to theoretical integrity, as exemplified by the seminal works of BriUinger (1981) and Hannan (1970) and the texts by Brockwell and Davis (1991) and Fuller (1995). The advent of more powerful computing, especially in the last three years, has provided both real data and new software that can take one considerably beyond the fitting of simple time domain models, such as have been elegantly described in the landmark work of Box and Jenkins (see Box et al., 1994). This book is designed to be useful as a text for courses in time series on several different levels and as a reference work for practitioners facing the analysis of time-correlated data in the physical, biological, and social sciences.

1 Characteristics of Time Series

 1.1 Introduction

 1.2 The Nature of Time Series Data

 1.3 Time Series Statistical Models

 1.4 Measures of Dependence: Autocorrelation and Cross-Correlation

 1.5 Stationary Time Series

 1.6 Estimation of Correlation

 1.7 Vector-Valued and Multidimensional Series

 Problems

2 Time Series Regression and Exploratory Data Analysis

 2.1 Introduction

 2.2 Classical Regression in the Time Series Context

 2.3 Exploratory Data Analysis

 2.4 Smoothing in the Time Series Context

 Problems

3 ARIMA Models

 3.1 Introduction

 3.2 Autoregressive Moving Average Models

 3.3 Difference Equations

 3.4 Autocorrelation and Partial Autocorrelation Functions

 3.5 Forecasting

 3.6 Estimation

 3.7 Integrated Models for Nonstationary Data

 3.8 Building ARIMA Models

 3.9 Multiplicative Seasonal ARIMA Models

 Problems

4 Spectral Analysis and Filtering

 4.1 Introduction

 4.2 Cyclical Behavior and Periodicity

 4.3 The Spectral Density

 4.4 Periodogram and Discrete Fourier Transform

 4.5 Nonparametric Spectral Estimation

 4.6 Multiple Series and Cross-Spectra

 4.7 Linear Filters

 4.8 Parametric Spectral Estimation

 4.9 Dynamic Fourier Analysis and Wavelets

 4.10 Lagged Regression Models

 4.11 Signal Extraction and Optimum Filtering

 4.12 Spectral Analysis of Multidimensional Series

 Problems

5 Additional Time Domain Topics

 5.1 Introduction

 5.2 Long Memory ARMA and Fractional Differencing

 5.3 GARCH Models

 5.4 Threshold Models

 5.5 Regression with Autocorrelated Errors

 5.6 Lagged Regression: Transfer Function Modeling

 5.7 Multivariate ARMAX Models

 Problems

6 State-Space Models

 6.1 Introduction

 6.2 Filtering, Smoothing, and Forecasting

 6.3 Maximum Likelihood Estimation

 6.4 Missing Data Modifications

 6.5 Structural Models: Signal Extraction and Forecasting

 6.6 ARMAX Models in State-Space Form

 6.7 Bootstrapping State-Space Models

 6.8 Dynamic Linear Models with Switching

 6.9 Nonlinear and Non-normal State-Space Models Using Monte Carlo Methods

 6.10 Stochastic Volatility

 6.11 State-Space and ARMAX Models for Longitudinal Data Analysis

 Problems

7 Statistical Methods in the Frequency Domain

 7.1 Introduction

 7.2 Spectral Matrices and Likelihood Functions

 7.3 Regression for Jointly Stationary Series

 7.4 Regression with Deterministic Inputs

 7.5 Random Coefficient Regression

 7.6 Analysis of Designed Experiments

 7.7 Discrimination and Cluster Analysis

 7.8 Principal Components and Factor Analysis

 7.9 The Spectral Envelope

 Problems

Appendix A: Large Sample Theory

 A.1 Convergence Modes

 A.2 Central Limit Theorems

 A.3 The Mean and Autocorrelation Functions

Appendix B: Time Domain Theory

 B.1 Hilbert Spaces and the Projection Theorem

 B.2 Causal Conditions for ARMA Models

 B.3 Large Sample Distribution of the AR(p) Conditional Least Squares Estimators

 B.4 The Wold Decomposition

Appendix C: Spectral Domain Theory

 C.1 Spectral Representation Theorem

 C.2 Large Sample Distribution of the DFT and Smoothed Periodogram

 C.3 The Complex Multivariate Normal Distribution

References

Index