Time Series: A Data Analysis Approach Using R, 1st Edition (Hardback) book cover

Time Series

A Data Analysis Approach Using R, 1st Edition

By Robert Shumway, David Stoffer

Chapman and Hall/CRC

259 pages

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pub: 2019-05-21
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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

About the Authors

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.

About the Series

Chapman & Hall/CRC Texts in Statistical Science

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Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General