Applied Time Series Analysis
CRC Press – 2011 – 564 pages
Virtually any random process developing chronologically can be viewed as a time series. In economics, closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested, Applied Time Series Analysis includes examples across a variety of fields, develops theory, and provides software to address time series problems in a broad spectrum of fields. The authors organize the information in such a format that graduate students in applied science, statistics, and economics can satisfactorily navigate their way through the book while maintaining mathematical rigor.
One of the unique features of Applied Time Series Analysis is the associated software, GW-WINKS, designed to help students easily generate realizations from models and explore the associated model and data characteristics. The text explores many important new methodologies that have developed in time series, such as ARCH and GARCH processes, time varying frequencies (TVF), wavelets, and more. Other programs (some written in R and some requiring S-plus) are available on an associated website for performing computations related to the material in the final four chapters.
"There is scarcely a standard technique that the reader will find left out … this book is highly recommended for those requiring a ready introduction to applicable methods in time series and serves as a useful resource for pedagogical purposes."
—International Statistical Review (2014), 82
"Current time series theory for practice is well summarized in this book."
—Emmanuel Parzen, Texas A&M University
"What an extraordinary range of topics covered, all very insightfully. I like [the authors’] innovations very much, such as the AR factor table."
—David Findley, U.S. Census Bureau (retired)
"… impressive coverage of the scope of time series analysis in both frequency and time domain … One unique feature of the book is the emphasis on factoring the AR polynomial function and its roots. … I commend the authors for having included a number of topics on nonstationary processes … an excellent textbook to adopt for a class and a good introductory book for a student who wants to embark on dissertation research in time series. … the book provides the reader with very good background material to be able to conduct practical and insightful data analysis and be able to comprehend the more theory-oriented books. There are many very good exercises in this book …"
—Hernando Ombao, Journal of the American Statistical Association, March 2013
"The book contains many illustrative examples, theorems with proofs, and applied and theoretical problems at the end of each chapter with real-life applications. Also, the book looks at generating realisations of the mentioned time series models via software packages such as GW-WINKS and R. The book’s material is very valuable and is well presented, so it represents a good reference at both undergraduate and postgraduate levels, and also a good source for all who are interested in time series analysis."
—Hassan S. Bakouch, Journal of Applied Statistics, 2012
Stationary Time Series
Stationary Time Series
Autocovariance and Autocorrelation Functions for Stationary Time Series
Estimation of the Mean, Autocovariance, and Autocorrelation for Stationary Time Series
Estimating the Power Spectrum and Spectral Density for Discrete Time Series
Time Series Examples
Introduction to Linear Filters
Stationary General Linear Processes
Wold Decomposition Theorem
ARMA Time Series Models
Moving Average 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
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
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
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
Proof of Kalman Recursion for Prediction and Filtering
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
Concluding Remarks on Wavelets
Appendix: Mathematical Preliminaries for This Chapter
Linear Chirp Processes
Henry L. Gray is a C.F. Frensley Professor Emeritus in the Department of Statistical Science at Southern Methodist University in Dallas, Texas.
Wayne A. Woodward is a professor and chair of the Department of Statistical Science at Southern Methodist University in Dallas, Texas.
Alan C. Elliott is a biostatistician in the Department of Clinical Sciences at the University of Texas Southwestern Medical Center in Dallas.