Description
Taylor & Francis Ltd Time Series A Data Analysis Approach Using R 2019 Edition by Robert Shumway, David Stoffer
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. 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