Tests of Random Walk: A Comparison of Bootstrap Approaches

This paper compares different versions of the multiple variance ratio test based on bootstrap techniques for the construction of empirical distributions. It also analyzes the crucial issue of selecting optimal block sizes when block bootstrap procedures are used. The comparison of the different approaches using Monte Carlo simulations leads to the conclusion that methodologies using block bootstrap methods present better performance for the construction of empirical distributions of the variance ratio test. Moreover, the results are highly sensitive to methods employed to test the null hypothesis of random walk.