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Abstract: A linear link between SandP 500 return and the change rate of the number ofnine-year-olds in the USA has been found. The return is represented by a sum ofmonthly returns during previous twelve months. The change rate of the specificage population is represented by moving averages. The period between January1990 and December 2003 is described by monthly population intercensal estimatesas provided by the US Census Bureau. Four years before 1990 are described usingthe estimates of the number of 17 year-olds shifted 8 years back. Theprediction of SandP 500 returns for the months after 2003, including those beyond2007, are obtained using the number of 3 year-olds between 1990 and 2003shifted by 6 years ahead and quarterly estimates of real GDP per capita. Aprediction is available for the period beyond 2007. There are two sharp dropsin the predicted returns - in 2007 and 2009, and one strong rally in 2008.Equivalently, SandP 500 index should drop in 2007 and 2009 to the level observedone year before. Potential link between SandP 500 returns and 9-year-oldpopulation is tested for cointegration. The Engle-Granger and Johansen testsdemonstrate the presence of a long-term equilibrium cointegrating relationbetween these variables. This makes valid standard statistical estimates.Correlation between the predicted and observed indices, including RMSdifference, linear regression, and VAR demonstrate good prediction accuracy attwo-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 periodbetween 1992 and 2003 is only 0.09 with standard deviation of the observedseries for the same period of 0.12 and the naive random walk RMS deference of0.18.

Author: Ivan O. Kitov, Oleg I. Kitov

Source: https://arxiv.org/

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