Weighted resampling of martingale difference arrays with applications

Abstract

In this paper the behaviour of linear resampling statistics in martingale difference arrays X_n,i,i≤k(n) is studied. It is shown that different bootstrap and permutation procedures work if the array (X_n,i)_i fulfils the conditions of a general central limit theorem. As an application we obtain amongst others resampling versions of the Kuan and Lee [20] test for the martingale difference hypothesis.