Exact prediction of S&P 500 returns
  A linear link between S&P 500 return and the change rate of the number of nine-year-olds in the USA has been found. The return is represented by a sum of monthly returns during previous twelve months. The change rate of the specific age population is represented by moving averages. The period between January 1990 and December 2003 is described by monthly population intercensal estimates as provided by the US Census Bureau. Four years before 1990 are described using the estimates of the number of 17 year-olds shifted 8 years back. The prediction of S&P 500 returns for the months after 2003, including those beyond 2007, are obtained using the number of 3 year-olds between 1990 and 2003 shifted by 6 years ahead and quarterly estimates of real GDP per capita. A prediction is available for the period beyond 2007. There are two sharp drops in the predicted returns - in 2007 and 2009, and one strong rally in 2008. Equivalently, S&P 500 index should drop in 2007 and 2009 to the level observed one year before. Potential link between S&P 500 returns and 9-year-old population is tested for cointegration. The Engle-Granger and Johansen tests demonstrate the presence of a long-term equilibrium (cointegrating) relation between these variables. This makes valid standard statistical estimates. Correlation between the predicted and observed indices, including RMS difference, linear regression, and VAR demonstrate good prediction accuracy at two-year horizon, when the prediction uses 7-year-olds instead of 9-year-olds. The RMS difference between the observed and predicted returns for the period between 1992 and 2003 is only 0.09 with standard deviation of the observed series for the same period of 0.12 and the naive (random walk) RMS deference of 0.18. 
Ivan O. Kitov, Oleg I. Kitov