Timing errors in digital transmission systems, such as maximum time interval error, are measured with data samples processed in a first stage to produce in real-time a first, time-varying series of measurements for a given parameter over observation intervals of a first magnitude. Each observation interval is many times longer than the sample period of the input series. Subsequent stages derive further measurements, corresponding to increasingly longer observation intervals, derived by treating previous observation intervals as sub-intervals. The first stage derives intermediate results for a predetermined interval and repeats for successive sub-intervals. The intermediate results are stored in a first first-in, first-out (FIFO) data set and updated at least once per sub-interval and the required parameter is derived. The second and subsequent stages similarly derive the required parameter corresponding to increasing observation interval magnitudes and update the measurements as data sets update.