On the discretisation error in the computation of the empirical characteristic function

Abstract

This paper analyses the discretisation error in computing the empirical characteristic function via the Fast Fourier Transform. Based on an interpretation of the discretisation scheme as a pre-smoothing, we obtain naturally a correction and possible generalizations, and derive exact and approximate formulas for the root mean square error involved. Some numerical evaluations are made, showing the accuracy of our approximate formula and the low value of the above root mean square error.