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