Time Series : A Data Analysis Approach Using R book cover
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Time Series
A Data Analysis Approach Using R




ISBN 9780367221096
Published May 21, 2019 by Chapman and Hall/CRC
259 Pages

 
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Book Description

The goals of this text are to develop the skills and an appreciation for the richness and versatility of modern time series analysis as a tool for analyzing dependent data. A useful feature of the presentation is the inclusion of nontrivial data sets illustrating the richness of potential applications to problems in the biological, physical, and social sciences as well as medicine. The text presents a balanced and comprehensive treatment of both time and frequency domain methods with an emphasis on data analysis.

Numerous examples using data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and the analysis of economic and financial problems. The text can be used for a one semester/quarter introductory time series course where the prerequisites are an understanding of linear regression, basic calculus-based probability skills, and math skills at the high school level. All of the numerical examples use the R statistical package without assuming that the reader has previously used the software.

Robert H. Shumway is Professor Emeritus of Statistics, University of California, Davis. He is a Fellow of the American Statistical Association and has won the American Statistical Association Award for Outstanding Statistical Application. He is the author of numerous texts and served on editorial boards such as the Journal of Forecasting and the Journal of the American Statistical Association.

David S. Stoffer is Professor of Statistics, University of Pittsburgh. He is a Fellow of the American Statistical Association and has won the American Statistical Association Award for Outstanding Statistical Application. He is currently on the editorial boards of the Journal of Forecasting, the Annals of Statistical Mathematics, and the Journal of Time Series Analysis. He served as a Program Director in the Division of Mathematical Sciences at the National Science Foundation and as an Associate Editor for the Journal of the American Statistical Association and the Journal of Business & Economic Statistics.

Table of Contents

1. Time Series Elements
 Introduction                             
 Time Series Data                          
 Time Series Models                         
 Problems                                 

2. Correlation and Stationary Time Series
 Measuring Dependence                      
 Stationarity                             
 Estimation of Correlation                      
Problems                                 

3. Time Series Regression and EDA
 Ordinary Least Squares for Time Series              
 Exploratory Data Analysis                     
 Smoothing Time Series                       
 Problems                                 

4. ARMA Models
 Autoregressive Moving Average Models              
 Correlation Functions                        
 Estimation                              
 Forecasting                             
 Problems                                 

5. ARIMA Models
 Integrated Models                         
 Building ARIMA Models                     
 Seasonal ARIMA Models                      
 Regression with Autocorrelated Errors *             
 Problems                                 

6. Spectral Analysis and Filtering
 Periodicity and Cyclical Behavior                 
 The Spectral Density                        
 Linear Filters *                           
 Problems                                 

7. Spectral Estimation
 Periodogram and Discrete Fourier Transform           
 Nonparametric Spectral Estimation                 
 Parametric Spectral Estimation                   
 Coherence and Cross-Spectra *                   
 Problems                                 

8. Additional Topics *
 GARCH Models                          
 Unit Root Testing                          
 Long Memory and Fractional Differencing            
 State Space Models                         
 Cross-Correlation Analysis and Prewhitening           
 Bootstrapping Autoregressive Models               
 Threshold Autoregressive Models                 
 Problems                                 

Appendix A R Supplement
Installing R                             
Packages and ASTSA                        
Getting Help                             
Basics                                
Regression and Time Series Primer                 
Graphics                               

Appendix B Probability and Statistics Primer
Distributions and Densities                     
Expectation, Mean and Variance                  
Covariance and Correlation                     
Joint and Conditional Distributions                 

Appendix C Complex Number Primer
Complex Numbers                         
Modulus and Argument                       
The Complex Exponential Function                
Other Useful Properties                       
Some Trigonometric Identities                   

Appendix D Additional Time Domain Theory
MLE for an AR()                         
Causality and Invertibility                     
ARCH Model Theory                        

Hints for Selected Exercises

 

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Author(s)

Biography

Robert H. Shumway is Professor Emeritus of Statistics, University of California, Davis. He is a Fellow of the American Statistical Association and has won the American Statistical Association Award for Outstanding Statistical Application. He is the author of numerous texts and served on editorial boards such as the Journal of Forecasting and the Journal of the American Statistical Association.

David S. Stoffer is Professor of Statistics, University of Pittsburgh. He is a Fellow of the American Statistical Association and has won the American Statistical Association Award for Outstanding Statistical Application. He is currently on the editorial boards of the Journal of Forecasting, the Annals of Statistical Mathematics, and the Journal of Time Series Analysis. He served as a Program Director in the Division of Mathematical Sciences at the National Science Foundation and as an Associate Editor for the Journal of the American Statistical Association and the Journal of Business & Economic Statistics.

Reviews

"The intended audience of the book are mathematics undergraduates taking a one semester course on time series. . . The authors frame learning time series primarily by extending concepts from linear models. Personally, I favour this approach, since it allows the book to clearly signpost similarities and differences between concepts in both topics and provides a natural learning progression from what most undergraduate students will already be familiar with . . .This book successfully delivers a practical tool-based approach to time series analysis at an introductory level, complementing the existing texts from the authors, which are aimed at a more advanced audience."
~Matthew Nunes, Journal Times Series Analysis

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