When modeling stock prices by decomposition into two CPI components and linear time trend we exercise two different time periods: after January 1994 and after June 2003. The reason for this separation is simple – the difference between individual CPI components is usually characterized by the presence of several linear trends. When linear trend in the difference between two defining CPI components has a pivot point relevant stock model also has a break in all coefficients. Therefore, we usually prefer to avoid this type of bias and limit our modeling to the period after June 2003 when all turns in many CPI difference did happen after the 2001 recession. This shorter modeling period significantly influences the resolution of the model and we would prefer to use longer time series when possible.
The model for Autodesk (ADSK) is an excellent example of the possibility to extend the modeling period back to 1994. The resulting model has a deterministic character and predicts the share price evolution at a several month horizon. Our model for ADSK is stable over the past year and is defined by expected indices: the consumer price index of motor vehicle maintenance and repair (MVR) and the index of information technology, hardware and software (IT). The latter defining index definitely has tight relations to ADSK.
The MVR index leads the share price by 5 months and the IT one - by 8 months. Figure 1 depicts the overall evolution of the difference between the involved indices. As discussed above, no change in the trend has been observed since 1994. Hence, the final share price model for ADSK should not be biased by the change in the trend.
These two defining CPI components provide the best fit model between June 2010 and December 2010. The MVR coefficient is negative and thus the increasing price of motor vehicle maintenance and repair causes the share price to fall. The IT index has a positive coefficient but the long-term decrease in this index also causes the share to fall. The slope of time trend is positive revealing the price tendency to increase over time. The best-fit 2-C model for an ADSK(t) share price is as follows:
ADSK(t) = -3.97MVR(t-5) + 2.18IT(t-8) + 35.25(t-1990) + 265.90
where t is calendar time.
The predicted and observed curves are presented in Figure 2. The residual error is $4.75 for the period between January 1994 and December 2010. The model provides a relatively good prediction of the share price in the past. Currently, the predicted price shows a strong tendency to rise. One should expect the ADSK price to grow fast in the first quarter of 2011.
Figure 1. Evolution of the difference between MVR and IT. No change in the long-term sustainable linear trend is observed.
Figure 2. Observed and predicted ADSK share prices.