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.

Tucker S. McElroy is Senior Time Series Mathematical Statistician at the U.S. Census Bureau, where he has contributed to developing time series research and software for the last 15 years. He has published more than 80 papers and is a recipient of the Arthur S. Flemming award (2011).

Dimitris N. Politis is Distinguished Professor of Mathematics at the University of California at San Diego, where he is also serving as Associate Director of the Halicioglu Data Science Institute. He has co-authored two research monographs and more than 100 journal papers. He is a recipient of the Tjalling C. Koopmans Econometric Theory Prize (2009-2011) and is Co-Editor of the Journal of Time Series Analysis.

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.

1. Introduction Time Series Data Cycles in Time Series Data Spanning and Scaling Time Series Time Series Regression and Autoregression Overview Exercises

2. The Probabilistic Structure of Time Series Random Vectors Time Series and Stochastic Processes Marginals and Strict Stationarity Autocovariance and Weak Stationarity Illustrations of Stochastic Processes Three Examples of White Noise Overview Exercises

3. Trends, Seasonality, and Filtering Nonparametric Smoothing Linear Filters and Linear Time Series Some Common Types of Filters Trends Seasonality Trend and Seasonality Together Integrated Processes Overview Exercises

4. The Geometry of Random Variables Vector Space Geometry and Inner Products L2(; P;F): The Space of Random Variables with Finite Second Moment Hilbert Space Geometry Projection in Hilbert Space Prediction of Time Series Linear Prediction of Time Series Orthonormal Sets and Infinite Projection Projection of Signals Overview Exercises

5. ARMA Models with White Noise Residuals Definition of the ARMA Recursion Difference Equations Stationarity and Causality of the AR(1) Causality of ARMA Processes Invertibility of ARMA Processes The Autocovariance Generating Function Computing ARMA Autocovariances via the MA Representation Recursive Computation of ARMA Autocovariances Overview Exercises

6. Time Series in the Frequency Domain The Spectral Density Filtering in the Frequency Domain Inverse Autocovariances Spectral Representation of Toeplitz Covariance Matrices Partial Autocorrelations Application to Model Identification Overview Exercises

7. The Spectral Representation The Herglotz Theorem The Discrete Fourier Transform The Spectral Representation Optimal Filtering Kolmogorov's Formula The Wold Decomposition Spectral Approximation and the Cepstrum Overview Exercises

8. Information and Entropy Introduction Events and Information…