I assume that the closing S&P 500 level of 1183 in October 2010 and its following growth to 1225 in November 2010 is not good news for the US stock market. Figures 1 and 2 update the previous versions published in this blog in September. Both Figures demonstrate that the difference between the predicted and observed curves has been increasing since September.
This observation raises a question on the following events. Our concern about possible repetition of the 1987 fall, if the index would continue its deviation from the predicted trend into October 2010 is on again. So, I see a danger of a severe panic on the stock market. Because Tuesday is a common day for such events, I cannot exclude that one of Tuesdays in the nearest future will end in a return of the observed curves to the predicted one.
There is also a chance that the population estimates underlying the prediction become wrong since September 2010. The methods of population projection and updates used by the Census Bureau are also not well predicted.
Below we repeat a mandatory part with a bit of mathematics for the readers interested in details of our model. The model is also presented in our working paper  and monograph .
The original model links the S&P 500 annual returns, Rp(t), to the number of nine-year-olds, N9. In order to extend the prediction in time we use the number of three-year-olds, N3, as a proxy to N9 and obtain a forecast at a six-year horizon:
Rp(t+6) = 100dlnN3(t) - 0.23 (1)
where Rp(t+6)is the S&P 500 return six years ahead (in 2010 one can foresee the returns in 2016). Figure 1 depicts germane S&P 500 returns, both actual one and that predicted by relationship (1). Both curves are coinciding in practical terms.
Because of the observed linear growth in N3 one can replace it with linear trends for the period between 2008 and 2011, as Figure 2 shows. This model predicts that the S&P 500 stock market index will be gradually decreasing at an average rate of 37 points per month. All fluctuations in N3, as observed in Figure 1, are smoothed in this linear representation.
Figure 1. Observed and predicted S&P 500 returns. The last point for the observed series is October 31, 2010.
Figure 2. The observed monthly closing level of the S&P 500 stock market index and the trend predicted from the number of nine-year-olds. The slope is of -37 points per month. The same but positive slope was observed between February 2009 and April 2010. The last point in the observed series is October 31, 2010. The deviation between the predicted and observed curves has been increasing since September 2010.