AMAT(t)= -2.89SEFV(t-2) + 2.21RPR(t-7) +2.48(t-1990) + 61.4
where SEFV in the index of food away from home leading the stock price by 2 months, RPR is the index of rent of primary residence leading by 7 months, (t-1990) is the elapsed time.
The predicted curve in Figure 1 actually leads the observed price by 2 (!) months, i.e. current readings of relevant CPI subcategories allow the prediction at a 2-month horizon. Figure 2 presents the residual error, with standard deviation of $1.23 for the period between July 2003 and April 2010
Figure 1. Observed and predicted share prices.