Time Series: A First Course with Bootstrap Starter provides an introductory course on time series analysis that satisfies the triptych of (i) mathematical completeness, (ii) computational illustration and implementation, and (iii) conciseness and accessibility to upper-level undergraduate and M.S. students. Basic theoretical results are presented in a mathematically convincing way, and the methods of data analysis are developed through examples and exercises parsed in R. A student with a basic course in mathematical statistics will learn both how to analyze time series and how to interpret the results.

The book provides the foundation of time series methods, including linear filters and a geometric approach to prediction. The important paradigm of ARMA models is studied in-depth, as well as frequency domain methods. Entropy and other information theoretic notions are introduced, with applications to time series modeling. The second half of the book focuses on statistical inference, the fitting of time series models, as well as computational facets of forecasting. Many time series of interest are nonlinear in which case classical inference methods can fail, but bootstrap methods may come to the rescue. Distinctive features of the book are the emphasis on geometric notions and the frequency domain, the discussion of entropy maximization, and a thorough treatment of recent computer-intensive methods for time series such as subsampling and the bootstrap. There are more than 600 exercises, half of which involve R coding and/or data analysis. Supplements include a website with 12 key data sets and all R code for the book's examples, as well as the solutions to exercises.

chapter Chapter 1|24 pages


chapter Chapter 2|28 pages

The Probabilistic Structure of Time Series

chapter Chapter 3|40 pages

Trends, Seasonality, and Filtering

chapter Chapter 4|35 pages

The Geometry of Random Variables

chapter Chapter 5|39 pages

ARMA Models with White Noise Residuals

chapter Chapter 6|37 pages

Time Series in the Frequency Domain

chapter Chapter 7|39 pages

The Spectral Representation [⋆]

chapter Chapter 8|32 pages

Information and Entropy [⋆]

chapter Chapter 9|46 pages

Statistical Estimation

chapter Chapter 10|59 pages

Fitting Time Series Models

chapter Chapter 11|30 pages

Nonlinear Time Series Analysis

chapter Chapter 12|51 pages

The Bootstrap