Bootstrap for Time Series

This book provides a rigorous, self-contained, and comprehensive treatment of bootstrap methods for time series. It develops a unified understanding of how and why these techniques work. Readers are guided through the key principles underlying the design of successful bootstrap procedures, the role of dependence structures in their construction, and the limitations that must be considered when applying the methods in practice.

After introducing the essential mathematical and statistical tools required for the study of bootstrap methods, the book covers both time-domain and frequency-domain approaches. Major methodologies are presented, including a model-based bootstrap, the autoregressive sieve bootstrap, various block bootstrap procedures, the dependent wild bootstrap, and subsampling. Periodogram-based bootstrap is also discussed, including the multiplicative periodogram bootstrap as well as other frequency-domain variants designed to capture the covariance of the periodogram ordinates. Numerous examples, simulations, and carefully developed proofs illustrate both the theoretical foundations and the practical performance of these methods. Particular emphasis is placed on methodological insights and mathematical rigor, enabling readers not only to understand existing techniques but also to develop valid bootstrap procedures for new classes of statistics and dependence structures.

Designed for graduate students, researchers, and practitioners in statistics, econometrics, mathematics, engineering, and the natural sciences, the book serves equally well as a textbook for graduate courses and as a reference for independent study. Supplemented by exercises and an appendix providing a concise overview of modern time series analysis, it offers a comprehensive foundation for understanding and applying bootstrap methods in time series settings.