An Introduction to Bootstrap Theory in Time Series Econometrics

This article provides an introduction to methods and challenges underlying application of the bootstrap in econometric modelling of economic and financial time series. Validity, or asymptotic validity, of the bootstrap is discussed as this is a key element in deciding whether the bootstrap is applicable in empirical contexts. That is, as detailed here, bootstrap validity relies on regularity conditions, which need to be verified on a case-by-case basis. To fix ideas, asymptotic validity is discussed in terms of the leading example of bootstrap-based hypothesis testing in the well-known first order auto-regressive model. In particular, bootstrap versions of classic convergence in probability and distribution, and hence of laws of large numbers and central limit theorems, are discussed as crucial ingredients to establish bootstrap validity. Regularity conditions and their implications for possible improvements in terms of (empirical) size and power for bootstrap-based testing, when compared to asymptotic testing, are illustrated by simulations. Following this, an overview of selected recent advances in the application of bootstrap methods in econometrics is also given