A modified BDS test

Abstract The BDS test is a test for detecting whether a random sequence is i.i.d. (independent and identically distributed). It has been used in economics and finance to examine whether a fitted time series model is adequate by examining whether the residual sequence is nearly i.i.d. Though the BDS test is widely used in the literature, it has a weakness of over-rejecting the null hypothesis even though the sample size T is as large as ( 100 , 1000 ) . In this study, we propose a modified BDS test (MBDS test) by removing some terms from the correlation integral, which is the foundation of the BDS test. Theoretical calculations and simulation results show that the MBDS test efficiently corrects the bias of the BDS test.