We estimated a price model for Wal-Mart Stores(WMT) three months ago. The model is based on the decomposition of a share price into a sum of two selected consumer price indices. This is a new model defined by the index of hospital and related services (HOSP) and the price index of miscellaneous personal services (MISS), as reported by the US BLS. The former CPI component leads the share price by 10 months and the latter one evolves in sync with the price. Figure 1 depicts the overall evolution of both involved indices through March 2011. A very specific feature of both indices is their linearity over time: they are close to straight lines.
In this post, we re-estimate the WMT share price using new data for the first quarter of 2011. This allows validating the initial model and demonstrating its reliability. The previously obtained defining components are the same and provide the best fit model between June 2010 and March 2010 with only one month change in the lag for the HOST index. All coefficients in (1) are only slightly different for the new model (see below). The slope of the time trend is negative. The best-fit 2-C model for WMT(t) is as follows:
WMT(t) = 0.50HOSP(t-10) + 1.42MISS(t) - 28.39(t-1990) – 158.12 (January 2011) (1)
WMT(t) = 0.46HOSP(t-9) + 1.49MISS(t) - 28.03(t-1990) – 165.50 (March 2011)
where t is calendar time. The predicted curve in Figure 2 evolves in sync with the observed price. The residual error is $2.15 for the period between June 2003 and March 2011. One can expect just slight variations around the $50 level since linear growth in HOSP and MISS is effectively compensated by the negative time trend in (1).
Figure 1. Evolution of the price of HOSP and MISS.
Figure 2. Observed and predicted WMT share prices.
Figure 3. Residual error of the model.