We have already presented a preliminary model for Ashland Inc (ASH). (The quantitative approach is described in .) Here we re-estimate the model using new BLS estimates of CPIs. Ashland is a chemical company in the S&P 500 list since 1983. The stock price was defined by the index of food without beverages (FB) and that of miscellaneous personal goods (MISG). Both indices might be directly related to major ASH products. Figure 1 depicts the overall evolution of both involved consumer price indices. The best-fit 2-C model for ASH(t) is as follows:
ASH(t) = -4.06FB(t-2) – 3.11MISG(t-7) + 24.11(t-1990) + 719.56
Actually, the predicted curve in Figure 2 leads the observed price by 2 months with the residual RMS error of $4.23 (see Figure 3) for the period between March 2003 and March 2011. The evolution of the observed and predicted prices is synchronized and the model does predict the share price in the past and foresees at a two month horizon.
Both indices had a period of no growth between 2008 and 2010 and the price was driven by the time trend with the slope of +24.11. This effect resulted in the total growth of $50 during these two years. A slow growth in food price restarted in the end of 2010 and the share price stalled. In February and March 2011, the index of food grew from 222.9 to 225.3, i.e. by 3 units. All in all, the share has to fall by approximately $6 in the next two months.
Figure 1. Evolution of the price of FB and MISG.
Figure 2. Observed and predicted ASH share prices.
Figure 3. Residual error of the model.
I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.