An analysis of a widely used version of the CUSUM tracking signal

Tracking signals are used to determine whether a sequence of forecasts is unbiased. We analyse a version of the CUSUM tracking signal that is based on the unsmoothed average mean absolute deviation of forecasting errors. We make the common assumption that demand values in different periods are independently, identically, and normally distributed. We show that, when forecast errors in different periods are also normal iid, this version of the tracking signal can indicate that the sequence is not unbiased even when it is unbiased. We suggest a simple modification to the tracking signal that serves to eliminate this flaw.