This is a regular revision of our stock pricing model as applied to Avery Dennison Corporation (AVY). We decompose the time series of a given share price into a weighted sum of two individual consumer price indices plus linear time trend and free term over an extended period of time. The best fit model has to provide the lowermost RMS residual and also do not change with time.
In April 2011, we presented an original model for Avery Dennison Corporation based on the consumer price index of food (F) and that of new and used motor vehicle (NUMV). In the original model, the former CPI component led the share price by 4 months and the latter one led by 2 months. Figure 1 depicts the evolution of both (NSA) CPIs through January 2012. The upper panel of Figure 2 displays the predicted and observed monthly closing prices (adjusted for splits and dividends) as of March 2011.
In September 2011, we revisited the model using the prices and CPIs for the period through September 2011. (The CPIs were available only for August 2011.) The principal result was that the underlying model is practically the same as six months before with the same time lags but slightly different coefficients. In March 2011, we predicted a fall in the price which actually happened. In September, we expected that AVY stocks would be falling by the end of 2011 down to $16 per share from the September closing level $25.08 (see the middle panel in Figure 2). This was not a good prediction.
Here we revisit the model using data through January 2012 (see the lower panel in Figure 2). The three best-fit models for AVY(t) are as follows
AVY(t) = -4.24F(t-4) – 3.23NUMV(t-2) + 23.29(t-1990) + 799.24 , March 2011
AVY(t) = -3.92F(t-4) – 2.70NUMV(t-2) + 21.60(t-1990) + 710.60 , September 2011
AVY(t) = -3.61(t-5) – 2.10NUMV(t-3) + 19.86(t-1990) + 622.01 , January 2012
where AVY(t) is a share price in US dolalrs, t is calendar time. Relevant coefficients are both negative. The slope of time trend is positive. There is some drift in all coefficients caused by the uncertainty in measurements of both the stock prices and CPIs and by a slight collinearity between the CPI difference and linear time trend. Nevertheless, all models provide a prediction at a two- to three-month horizon.
The currently predicted curve in Figure 2 leads the observed price by 3 months with the residual error of $2.81 ($2.57 in September) for the period between July 2003 and January 2012. The model residual for the same period is shown in Figure 3. We expect the actual price to have a slight negative correction in the near future and the predicted curve to grow up in order to close the gap between the predicted and observed prices. The residual in Figure 3 has to return to 0. This might be accompanied by a slight fall in food prices.
Figure 1. Evolution of the price of F and NUMV.
Figure 2. Observed and predicted AVY share prices. Upper panel – March 2011; middle panel – September 2011; lower panel – January 2012.
Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.81. Currently, the price is slightly overestimated.