The BDS test and delay time

One of the most popular tests for detecting non-linear structure is the BDS test. This test is based on the correlation integral, and some studies have proved the sensitivity of this concept in relation to the choice of one particular parameter: delay time. However, the BDS test considers fixed delay time equal to one. In this paper it is investigated whether a flexible choice of delay time might improve the capacity of the BDS test. It is shown that the BDS-G test (generalized BDS test, including delay time choice) can capture non-linearities that are undetected by the classical BDS test. Finally, the robustness of the BDS-G test in the presence of noise is analysed.