TY - UNPB

T1 - An Introduction to Bootstrap Theory in Time Series Econometrics

AU - Cavaliere, Giuseppe

AU - Nielsen, Heino Bohn

AU - Rahbek, Anders

PY - 2020/5/28

Y1 - 2020/5/28

N2 - 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.

AB - 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.

KW - Bootstrap Theory; Bootstrap Implementation; Econometric Time Series Analysis; Testing; Asymptotic Theory; Auto-regressive Models

KW - Bootstrap Theory

KW - Bootstrap Implementation

KW - Econometric Time Series Analysis

KW - Testing

KW - Asymptotic Theory

KW - Auto-regressive Models

KW - C12

KW - C13

KW - C15

KW - C22

KW - C32

KW - C50

U2 - 10.2139/ssrn.3589144

DO - 10.2139/ssrn.3589144

M3 - Working paper

T3 - University of Copenhagen. Institute of Economics. Discussion Papers (Online)

BT - An Introduction to Bootstrap Theory in Time Series Econometrics

ER -