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Is complemented by an R package, tswge, available on CRAN which contains functions and over 100 real and simulated data sets to accompany the book.


Comments about Applied Time Series Analysis

“What an extraordinary range of topics this book covers, all very insightfully. I like [the authors’] innovations very much, including the AR factor table.” –David Findley, Senior Mathematical Statistician, US Census Bureau (retired)

"… impressive coverage of the scope of time series analysis in both frequency and time domain … … I commend the authors for having included a number of topics on nonstationary processes (e.g., time-varying spectrum, wavelets), excellent textbook …” —Hernando Ombao, Journal of the American Statistical Association

Information about 1st edition and GW WINKS


This is a support site for the book:


Applied Time Series Analysis with R Second Edition

Wayne A. Woodward, Southern Methodist University, Dallas, Texas, USA; Henry L. Gray, Southern Methodist University, Dallas, Texas, USA; Alan Elliott, Southern Methodist University, Dallas, Texas, USA

  • Price: $109.95
  • Hardcover: 630 pages
  • Publisher: CRC Press; 2 edition (January 9, 2017)
  • Language: English
  • ISBN-10: 1498734227
  • ISBN-13: 978-1498734226


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 with R, Second Edition includes examples across a variety of fields, develops theory, and provides an R-based software package in CRAN (tswge) to aid in addressing time series problems in a broad spectrum of fields. The material is organized in an optimal format for graduate students in statistics as well as in the natural and social sciences to learn to use and understand the tools of applied time series analysis.


  • Gives readers the ability to actually solve significant real-world problems
  • Addresses many types of nonstationary time series and cutting-edge methodologies
  • Promotes understanding of the data and associated models rather than viewing the series as the output of a "black box"
  • Over 150 exercises and extensive support for instructors

New to the Second Edition

The second edition has several enhancements that make it an ideal text for a stand-alone one semester or a two semester course in applied time series analysis.  New features include:

  • An accompanying, easy to use  R package that includes 50+ functions for analyzing time series data and producing associated graphical presentations
  • Many additional real-world data sets, all of which are included in the accompanying R package.  The package contains about 100 data sets (real and simulated).
  • Discusses new advances in the analysis of long memory and data with time-varying frequencies (TVF).

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
π-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 white noise variance
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 Building
Residual Analysis
Stationarity versus Nonstationarity
Signal-plus-Noise versus Purely Autocorrelation-Driven Models
Checking Realization Characteristics
Comprehensive Analysis of Time Series Data

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

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
Testing for long memory
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

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