On the errors involved in computing the empirical characteristic function

This paper considers discretisation errors involved in using the Fast Fourier Transform to compute the empirical characteristic function efficiently. A simple improvement to the usual histogram discretisation scheme is shown to reduce the mean square error considerably, as the grid size tends to zero. Simulation results show that the improvement is just as good in practical cases. The theoretical results are applied to the efficient calculation of kernel density estimates, described in Silverman (1982).