Introduction to Time Series Modeling with Applications in R (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
Preface for Second Edition
R and the Time Series Modeling Package TSSS
1. Introduction and Preparatory Analysis
	1.1 Time Series Data
	1.2 Classification of Time Series
	1.3 Objectives of Time Series Analysis
	1.4 Pre-Processing of Time Series
		1.4.1 Transformation of variables
		1.4.2 Differencing
		1.4.3 Month-to-month basis and year-over-year
		1.4.4 Moving average
	1.5 Organization of This Book
2. The Covariance Function
	2.1 The Distribution of Time Series and Stationarity
	2.2 The Autocovariance Function of Stationary Time Series
	2.3 Estimation of the Autocovariance and Autocorrelation Functions
	2.4 Multivariate Time Series and Scatterplots
	2.5 Cross-Covariance Function and Cross-Correlation Function
3. The Power Spectrum and the Periodogram
	3.1 The Power Spectrum
	3.2 The Periodogram
	3.3 Averaging and Smoothing of the Periodogram
	3.4 Computational Method of Periodogram
	3.5 Computation of the Periodogram by Fast Fourier Transform
4. Statistical Modeling
	4.1 Probability Distributions and Statistical Models
	4.2 K-L Information and Entropy Maximization Principle
	4.3 Estimation of the K-L Information and the Log-Likelihood
	4.4 Estimation of Parameters by the Maximum Likelihood Method
	4.5 AIC (Akaike Information Criterion)
		4.5.1 Evaluation of C1
		4.5.2 Evaluation of C3
		4.5.3 Evaluation of C2
		4.5.4 Evaluation of C and AIC
	4.6 Transformation of Data
5. The Least Squares Method
	5.1 Regression Models and the Least Squares Method
	5.2 The Least Squares Method Based on the Householder Transformation
	5.3 Selection of Order by AIC
	5.4 Addition of Data and Successive Householder Reduction
	5.5 Variable Selection by AIC
6. Analysis of Time Series Using ARMA Models
	6.1 ARMA Model
	6.2 The Impulse Response Function
	6.3 The Autocovariance Function
	6.4 The Relation Between AR Coefficients and PARCOR
	6.5 The Power Spectrum of the ARMA Process
	6.6 The Characteristic Equation
	6.7 The Multivariate AR Model
7. Estimation of an AR Model
	7.1 Fitting an AR Model
	7.2 Yule-Walker Method and Levinson’s Algorithm
	7.3 Estimation of an AR Model by the Least Squares Method
	7.4 Estimation of an AR Model by the PARCOR Method
	7.5 Large Sample Distribution of the Estimates
	7.6 Estimation of Multivariate AR Model by the Yule-Walker Method
	7.7 Estimation of Multivariate AR Model by the Least Squares Method
8. The Locally Stationary AR Model
	8.1 Locally Stationary AR Model
	8.2 Automatic Partitioning of the Time Interval into an Arbitrary Number of Subintervals
	8.3 Precise Estimation of the Change Point
	8.4 Posterior Probability of the Change Point
9. Analysis of Time Series with a State-Space Model
	9.1 The State-Space Model
	9.2 State Estimation via the Kalman Filter
	9.3 Smoothing Algorithms
	9.4 Long-Term Prediction of the State
	9.5 Prediction of Time Series
	9.6 Likelihood Computation and Parameter Estimation for Time Series Models
	9.7 Interpolation of Missing Observations
10. Estimation of the ARMA Model
	10.1 State-Space Representation of the ARMA Model
	10.2 Initial State Distribution for an AR Model
	10.3 Initial State Distribution of an ARMA Model
	10.4 Maximum Likelihood Estimates of an ARMA Model
	10.5 Initial Estimates of Parameters
11. Estimation of Trends
	11.1 The Polynomial Trend Model
	11.2 Trend Component Model – Model for Gradual Changes
	11.3 Trend Model
12. The Seasonal Adjustment Model
	12.1 Seasonal Component Model
	12.2 Standard Seasonal Adjustment Model
	12.3 Decomposition Including a Stationary AR Component
	12.4 Decomposition Including a Trading-Day Effect
13. Time-Varying Coefficient AR Model
	13.1 Time-Varying Variance Model
	13.2 Time-Varying Coefficient AR Model
	13.3 Estimation of the Time-Varying Spectrum
	13.4 The Assumption on System Noise for the Time-Varying Coefficient AR Model
	13.5 Abrupt Changes of Coefficients
14. Non-Gaussian State-Space Model
	14.1 Necessity of Non-Gaussian Models
	14.2 Non-Gaussian State-Space Models and State Estimation
	14.3 Numerical Computation of the State Estimation Formula
	14.4 Non-Gaussian Trend Model
	14.5 Non-symmetric Distribution – A Time-Varying Variance Model
	14.6 Applications of the Non-Gaussian State-Space Model
		14.6.1 Processing of the outliers by a mixture of Gaussian distributions
		14.6.2 A nonstationary discrete process
		14.6.3 A direct method of estimating the time-varying variance
		14.6.4 Nonlinear state-space models
15. Particle Filter
	15.1 The Nonlinear Non-Gaussian State-Space Model and Approximations of Distributions
	15.2 Particle Filter
		15.2.1 One-step-ahead prediction
		15.2.2 Filtering
		15.2.3 Algorithm for the particle filter
		15.2.4 Likelihood of a model
		15.2.5 On the re-sampling method
		15.2.6 Numerical examples
	15.3 Particle Smoothing Method
	15.4 Nonlinear Smoothing
16. Simulation
	16.1 Generation of Uniform Random Numbers
	16.2 Generation of White Noise
		16.2.1 x2 distribution
		16.2.2 Cauchy distribution
		16.2.3 Arbitrary distribution
	16.3 Simulation of ARMA models
	16.4 Simulation Using a State-Space Model
	16.5 Simulation with the Non-Gaussian State-Space Model
Appendix A: Algorithms for Nonlinear Optimization
Appendix B: Derivation of Levinson’s Algorithm
Appendix C: Derivation of the Kalman Filter and Smoother Algorithms
	C.1 Kalman Filter
	C.2 Smoothing
Appendix D: Algorithm for the Particle Filter
	D.1 One-Step-Ahead Prediction
	D.2 Filter
	D.3 Smoothing
Bibliography
Index