Time Series Analysis and Its Applications: With R Examples

Preface to the Fifth Edition
Preface to the Fourth Edition
Preface to the Third Edition
Biography
1 Characteristics of Time Series
	1.1 The Nature of Time Series Data
	1.2 Time Series Statistical Models
	1.3 Measures of Dependence
	1.4 Stationary Time Series
	1.5 Estimation of Correlation
	1.6 Vector-Valued and Multidimensional Series
	1.7 Random Number Generation
	Problems
2 Time Series Regression and Exploratory Data Analysis
	2.1 Classical Regression in the Time Series Context
	2.2 Exploratory Data Analysis
	2.3 Smoothing in the Time Series Context
	Problems
3 ARIMA Models
	3.1 Autoregressive and Moving Average Models
		3.1.1 Introduction to Autoregressive Models
		3.1.2 Introduction to Moving Average Models
		3.1.3 Autoregressive Moving Average Models
	3.2 Difference Equations
	3.3 Autocorrelation and Partial Autocorrelation
		3.3.1 ACF
		3.3.2 PACF
	3.4 Forecasting
		3.4.1 Best Linear Prediction
		3.4.2 Forecasting ARMA Processes
	3.5 Estimation
		3.5.1 Method of Moments
		3.5.2 Maximum Likelihood and Least Squares Estimation
		3.5.3 Gauss–Newton
	3.6 Integrated Models for Nonstationary Data
	3.7 Building ARIMA Models
	3.8 Regression with Autocorrelated Errors
	3.9 Multiplicative Seasonal ARIMA Models
	Problems
4 Spectral Analysis and Filtering
	4.1 Cyclical Behavior and Periodicity
	4.2 The Spectral Density
	4.3 Periodogram and Discrete Fourier Transform
	4.4 Nonparametric Spectral Estimation
		4.4.1 Smoothing the Periodogram
		4.4.2 Tapering
	4.5 Parametric Spectral Estimation
	4.6 Multiple Series and Cross-Spectra
	4.7 Linear Filters
	4.8 Lagged Regression Models
	4.9 Signal Extraction and Optimum Filtering
	4.10 Spectral Analysis of Multidimensional Series
	4.11 Structural Breaks
		4.11.1 AutoParm: A Parametric Approach
		4.11.2 AutoSpec: A Nonparametric Approach
		4.11.3 Genetic Algorithm
	Problems
5 Additional Time Domain Topics
	5.1 Long Memory ARMA and Fractional Differencing
	5.2 Unit Root Testing
	5.3 GARCH Models
	5.4 Threshold Models
	5.5 Multivariate ARMAX Models
		5.5.1 VAR Models
		5.5.2 VARMA Models
	Problems
6 State-Space Models
	6.1 Linear Gaussian Model
	6.2 Filtering, Smoothing, and Forecasting
	6.3 Maximum Likelihood Estimation
		6.3.1 Newton–Raphson
		6.3.2 EM Algorithm
			Including Inputs
		6.3.3 Asymptotic Distribution of the MLEs
	6.4 Missing Data Modifications
	6.5 Structural Models: Signal Extraction and Forecasting
	6.6 State-Space Models with Correlated Errors
		6.6.1 ARMAX Models
		6.6.2 Multivariate Regression with Autocorrelated Errors
	6.7 Bootstrapping State-Space Models
	6.8 Smoothing Splines and the Kalman Smoother
	6.9 Hidden Markov Models and Switching Autoregression
	6.10 Dynamic Linear Models with Switching
	6.11 Bayesian Analysis of State-Space Models
		6.11.1 Gibbs Sampler
		6.11.2 Particle Methods
	6.12 Stochastic Volatility
		6.12.1 Bayesian Analysis
		6.12.2 Classical Analysis
		6.12.3 Stochastic Volatility with Feedback
	6.13 Kalman Filter and Smoother Scripts
	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
		7.3.1 Estimation of the Regression Function
		7.3.2 Estimation Using Sampled Data
		7.3.3 Tests of Hypotheses
	7.4 Regression with Deterministic Inputs
		7.4.1 Estimation of the Regression Relation
		7.4.2 Tests of Hypotheses
	7.5 Random Coefficient Regression
		7.5.1 Estimation of the Regression Relation
		7.5.2 Detection and Parameter Estimation
	7.6 Analysis of Designed Experiments
		7.6.1 Equality of Means
		7.6.2 An Analysis of Variance Model
		7.6.3 Simultaneous Inference
		7.6.4 Multivariate Tests
	7.7 Discriminant and Cluster Analysis
		7.7.1 The General Discrimination Problem
		7.7.2 Frequency Domain Discrimination
		7.7.3 Measures of Disparity
		7.7.4 Cluster Analysis
	7.8 Principal Components and Factor Analysis
		7.8.1 Principal Components
		7.8.2 Factor Analysis
	7.9 The Spectral Envelope
		7.9.1 Categorical Time Series
		7.9.2 Real-Valued Time Series
	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 Law of Iterated Expectations
	B.3 Causal Conditions for ARMA Models
	B.4 Large Sample Distribution of the AR Conditional Least Squares Estimators
	B.5 The Wold Decomposition
Appendix C Spectral Domain Theory
	C.1 Spectral Representation Theorems
	C.2 Large Sample Distribution of the Smoothed Periodogram
	C.3 The Complex Multivariate Normal Distribution
	C.4 Integration
		C.4.1 Riemann–Stieltjes Integration
		C.4.2 Stochastic Integration
	C.5 Spectral Analysis as Principal Component Analysis
	C.6 Parametric Spectral Estimation
	C.7 Cumulants and Higher-Order Spectra
Appendix D Complex Number Primer
	D.1 Complex Numbers
	D.2 Modulus and Argument
	D.3 The Complex Exponential Function
	D.4 Other Useful Properties
	D.5 Some Trigonometric Identities
	D.6 Matrix Representation
References
Index