Two years ago we presented a quarterly report of the performance of our share price model for Hewlett Packard (NYSE:HPQ). This company provides a good example of a successful share price prediction at a several month horizon. We have already published our predictions at a four month horizon five times (July 2010, January 2011, March 2011, July 2011, and September 2011, February 2012). This is a revision of the original model which validates our concept of share pricing.
All predictions were based on our concept of share pricing as decomposition into a weighted sum of two CPI components. The intuition behind our concept is simple; a faster growth in the CPI directly related to the share price (e.g. energy consumer price for energy companies) relative to some independent and dynamic reference (e.g. some goods and services which price does not depend on energy) should be manifested in a higher pricing power for the company. Our model selects (using the LSQ method) a defining CPI and the best reference index from a set of 92 CPI with estimates started before 2000. This set is fixed what is important for model stability. Both CPIs for a given model must define the studied price for at least 8 months in a row, i.e. the model has to be the same for a relatively long time: the longer – the better. Our model for HPQ was stable between 2010 and 2012 and showed an excellent predictive power at a four month horizon for more than 30 months without gaps. The current revision extends the model by another 24 months of successful prediction. Altogether, the model is valid since the beginning of 2010 with just minor changes.
Originally, the long term model for HPQ share price was defined by the index of food without beverages (FB) and that of rent of primary residency (RPR). The former CPI component led the share price by 4 months and the latter one led by 5 months. The current model includes slightly different components of the CPI: the index of other food at home (OFH) and the index of housing operations (HO), which are quite similar in the overall evolution to the originally used components. Figure 1 depicts the overall evolution of all four involved indices through February 2014. Below we present five best-fit models for HPQ(t) obtained at different times:
HPQ(t) = -3.20FB(t-4) + 2.91RPR(t-5) + 3.64(t-1990) - 50.82, July 2010
HPQ(t) = -3.34FB(t-4) + 3.41RPR(t-5) + 0.51(t-1990) - 85.44, June 2011
HPQ(t) = -3.46FB(t-4) + 3.68RPR(t-5) – 0.72(t-1990) - 99.88, September 2011
HPQ(t) = -3.40FB(t-5) + 3.60RPR(t-6) – 0.57(t-1990) – 97.72, December 2011
HPQ(t) = -3.27FB(t-4) + 3.46RPR(t-5) – 0.39(t-1990) – 95.71, February 2012
HPQ(t) = -1.58OFH(t-4)+3.15HO(t-11) – 4.03(t-2000) – 89.35, February 2014
where HPQ(t) is the price in US dollars, t is calendar time. All coefficients have been slightly drifting but very close. This process expresses the trade-off between the linear trend in the difference between the defining CPIs and the time trend term in the above equtions.
Currently, HPQ price is predicted to decline a little in March and April 2014. This fall is a marginal one ($1) and lays within the uncertainty bounds of the model prediction – standard deviation of the model residual is $2.9 since 2003. Figure 3 depicts the model error. It is worth noting that the residual is an I(0) process that means that the predicted and observed prices are cointegrated time series. This makes all statistical estimates valid.
Figure 1. Evolution of the price of OFH and HO relative to FB and RPR.
Figure 2. Observed and predicted HPQ share price.
Figure 3. The model residual error; sterr=$2.91.