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.
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
