On the bias of Croston's forecasting method

Croston's forecasting method (CR) has been shown to be appropriate in dealing with intermittent demand items. The method, however, suffers from a positive bias as discussed by Syntetos and Boylan [Syntetos, A.A., Boylan, J.E., 2005a. The accuracy of intermittent demand estimates. International Journal of Forecasting 21, 303-314] who proposed a modification (SB). Unfortunately, the modification ignores the damping effect on the bias of the probability that a demand occurs. This leads to overcompensation and a negative bias, which can in fact be larger than the positive bias of the original method. Syntetos [Syntetos, A.A., 2001. Forecasting for Intermittent Demand, Unpublished Ph.D thesis, Buckinghamshire Chilterns University College, Brunel University] proposed another modification (SY) that takes the damping effect into account, thereby reducing the bias. However, he eventually disregarded it from the empirical analysis, because of the analytical results that SY never dominates SB as well as CR when both bias and variance are considered. Levén and Segerstedt [Levén, E., Segerstedt, A., 2004. Inventory control with a modified Croston procedure and Erlang distribution. International Journal of Production Economics 90, 361-367] also proposed a modified Croston method (LS) and claimed it to be unbiased. We compare all four methods in a numerical study. Our results strengthen the finding from Boylan and Syntetos [Boylan, J.E., Syntetos A.A., 2007. The accuracy of a modified Croston procedure. International Journal of Production Economics 107, 511-517] that LS suffers from a much more severe bias that the other methods. They also confirm SB as the best method when the Mean Square Error is considered. However, SY has a much smaller average absolute bias of 1% compared to 5% for the SB method. From an inventory control point of view, this is an important advantage of the SY method, since biases distort calculations of the expected lead time demand as well as safety stock calculations. An additional advantage of the SY method is its robust performance over the range of parameter values that we considered. Based on these results, we suggest that the SY method should receive more consideration as an alternative to CR and SB.