Forecasting via Fokker–Planck Using Conditional Probabilities

Abstract

Using a closed solution to a Fokker–Planck equation model of a time series, a probability distribution for the next observation is developed. This pdf has one free parameter, b. Various approaches to selecting this parameter have been explored: most recent value, weighted moving average, etc. Here, we explore using a conditional probability distribution for this parameter b, based upon the most recent observation. These methods are tested against some real-world product sales for both a one-step ahead and a two-step ahead forecast. Significant reduction in safety stock levels is found versus an ARMA approach, without a significant increase in out-of-stocks.

Appendix

Fokker–Planck Distributions $\mathbf {W}_{\mathbf {b}}$ Versus Normal (AR(7), $\hat{\mathbf {s}}_{\mathbf {e}}$ )

See Figs. 3 and 4.

Fig. 3

Plot of (i) $W_b$ and (ii) Normal (AR(7), $\hat{s}_e$)—(ii) is the wider graph b has its smallest value: $b_1$

Fig. 4

Plot of (i) $W_b$ and (ii) Normal (AR(7), $\hat{s}_e$)—(ii) is the wider graph b has its fourth value: $b_4$