Time Series

A First Course with Bootstrap Starter

Dimitris N. Politis, Tucker S. McElroy

• Publisher: Chapman and Hall/CRC
• Year: 2019
• eBook ISBN: 9780429527227
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• 1 Introduction
• 2 The Probabilistic Structure of Time Series
• 3 Trends, Seasonality, and Filtering
• 4 The Geometry of Random Variables
• 5 ARMA Models with White Noise Residuals
• 6 Time Series in the Frequency Domain
• 7 The Spectral Representation [*]
• 8 Information and Entropy [*]
• 9 Statistical Estimation
• 10 Fitting Time Series Models
• 11 Nonlinear Time Series Analysis
• 12 The Bootstrap
• A Probability
• B Mathematical Statistics
• C Asymptotics
• D Fourier Series
• E Stieltjes Integration
• Index