Validity of handwriting movement data recorded with digitizing tablets is poorly reflected by manufacturer's specifications. Actual errors of positional data are in fact in a critical range, in particular when time derivatives are calculated. Because differentiation magnifies errors in the displacement data, data smoothing becomes crucial. A new method for smoothing and differentiating noisy handwriting movement data is proposed. Non-parametric estimation of regression functions using kernel estimates generally offers simple application and extremely fast calculation. Assessing simulation data the efficiency of the procedure was investigated and compared with butterworth filters and finite impulse response (FIR) filters. Kernel estimates show a slightly elevated bias, but strongly reduced residual variance in the velocity and acceleration signals. The overall smoothing behaviour of kernel estimates is better than butterworth filters and very similar to FIR filters, if their transition band is chosen appropriately.