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Applied Time Series Analysis

Wayne A. Woodward, Henry L. Gray, and Alan C. Elliott
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
Statistics: Textbooks and Monographs
We do not plan to review this book.

Stationary Time Series
Time Series
Stationary Time Series
Autocovariance and Autocorrelation Functions for Stationary Time Series
Estimation of the Mean, Autocovariance, and Autocorrelation for Stationary Time Series
Power Spectrum
Estimating the Power Spectrum and Spectral Density for Discrete Time Series
Time Series Examples

Linear Filters
Introduction to Linear Filters
Stationary General Linear Processes
Wold Decomposition Theorem
Filtering Applications

ARMA Time Series Models
Moving Average Processes
Autoregressive Processes
Autoregressive–Moving Average Processes
Visualizing Autoregressive Components
Seasonal ARMA(p,q)x(Ps,Qs)s Models
Generating Realizations from ARMA(p,q) Processes

Other Stationary Time Series Models
Stationary Harmonic Models
ARCH and GARCH Models

Nonstationary Time Series Models
Deterministic Signal-Plus-Noise Models
ARIMA(p,d,q) and ARUMA(p,d,q) Models
Multiplicative Seasonal ARUMA(p,d,q) x (Ps,Ds,Qs)s Model
Random Walk Models
G-Stationary Models for Data with Time-Varying Frequencies

Mean Square Prediction Background
Box–Jenkins Forecasting for ARMA(p,q) Models
Properties of the Best Forecast Xto(l)
pi-Weight Form of the Forecast Function
Forecasting Based on the Difference Equation
Eventual Forecast Function
Probability Limits for Forecasts
Forecasts Using ARUMA(p,d,q) Models
Forecasts Using Multiplicative Seasonal ARUMA Models
Forecasts Based on Signal-plus-Noise Models

Parameter Estimation
Preliminary Estimates
Maximum Likelihood Estimation of ARMA( p,q) Parameters
Backcasting and Estimating σ2a
Asymptotic Properties of Estimators
Estimation Examples Using Data
ARMA Spectral Estimation
ARUMA Spectral Estimation

Model Identification
Preliminary Check for White Noise
Model Identification for Stationary ARMA Models
Model Identification for Nonstationary ARUMA(p,d,q) Models
Model Identification Based on Pattern Recognition

Model Building
Residual Analysis
Stationarity versus Nonstationarity
Signal-plus-Noise versus Purely Autocorrelation-Driven Models
Checking Realization Characteristics
Comprehensive Analysis of Time Series Data: A Summary

Vector-Valued (Multivariate) Time Series
Multivariate Time Series Basics
Stationary Multivariate Time Series
Multivariate (Vector) ARMA Processes
Nonstationary VARMA Processes
Testing for Association between Time Series
State-Space Models
Proof of Kalman Recursion for Prediction and Filtering

Long-Memory Processes
Long Memory
Fractional Difference and FARMA Models
Gegenbauer and GARMA Processes
k-Factor Gegenbauer and GARMA Models
Parameter Estimation and Model Identification
Forecasting Based on the k-Factor GARMA Model
Modeling Atmospheric CO2 Data Using Long-Memory Models

Shortcomings of Traditional Spectral Analysis for TVF Data
Methods That Localize the ‘‘Spectrum’’ in Time
Wavelet Analysis
Wavelet Packets
Concluding Remarks on Wavelets
Appendix: Mathematical Preliminaries for This Chapter

G-Stationary Processes
Generalized-Stationary Processes
M-Stationary Processes
G(λ)-Stationary Processes
Linear Chirp Processes
Concluding Remarks