An Introduction to Bootstrap Theory in Time Series Econometrics

While often simple to implement in practice, application of the bootstrap in econometric modeling of economic and financial time series requires establishing validity of the bootstrap. Establishing bootstrap asymptotic validity relies on verifying often nonstandard regularity conditions. In particular, bootstrap versions of classic convergence in probability and distribution, and hence of laws of large numbers and central limit theorems, are critical ingredients. Crucially, these depend on the type of bootstrap applied (e.g., wild or independently and identically distributed (i.i.d.) bootstrap) and on the underlying econometric model and data. Regularity conditions and their implications for possible improvements in terms of (empirical) size and power for bootstrap-based testing differ from standard asymptotic testing, which can be illustrated by simulations.

TESTING FOR PHASE SYNCHRONIZATION

We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series.