According to , the model for 3M Company (MMM) is defined by the index of dairy products (DAIRY- CUUS0000SEFJ) and that of public transportation (TPU- CUUS0000SETG). The former CPI component leads the share price by 10 months and the latter one leads by 6 months. Figure 1 depicts the overall evolution of both involved indices. However, both defining components provide the best fit model between August 2009 and June 2010. Both coefficients are negative and only positive time trend with slope of 8.7 has been compensating the negative input of both CPIs .
So, the best-fit 2-C model for MMM(t) is as follows:
MMM(t) = -0.74DAIRY(t-10) – 0.54TPUP(t-6) + 8.70(t-2000) + 180.88
The predicted curve in Figure 2 leads the observed price by 6 (!) months with the residual error of $3.79 for the period between July 2003 and June 2010. In other words, the price of a MMM share is completely defined by the behaviour of the two CPI components.
The model does predict the share price in the past and foresee a significant fall in the last quarter of 2010, i.e. through December 2010. It will be in line with the overall fall in the S&P 500 in 2010.
Figure 1. Evolution of the price of DAIRY and TPU.
Figure 2. Observed and predicted MMM share prices. Original prediction is shown by red line. Black diamonds present the original line shifted 6 months ahead.
Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $3.79. The largest errors were observed in 2005 and 2006.
Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.