Kitov, Ivan and Kitov, Oleg (2007): Exact prediction of S&P 500 returns.

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Abstract
A linear link between S&P 500 return and the change rate of the number of nineyearolds 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 yearolds 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 yearolds 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 9yearold population is tested for cointegration. The EngleGranger and Johansen tests demonstrate the presence of a longterm 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 twoyear horizon, when the prediction uses 7yearolds instead of 9yearolds. 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 naïve (random walk) RMS deference of 0.18.
Item Type:  MPRA Paper 

Original Title:  Exact prediction of S&P 500 returns 
Language:  English 
Keywords:  S&P 500, returns, prediction, population, economic growth 
Subjects:  D  Microeconomics > D5  General Equilibrium and Disequilibrium > D53  Financial Markets G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice ; Investment Decisions F  International Economics > F4  Macroeconomic Aspects of International Trade and Finance > F47  Forecasting and Simulation: Models and Applications 
Item ID:  6056 
Depositing User:  Ivan Kitov 
Date Deposited:  03. Dec 2007 05:19 
Last Modified:  12. Feb 2013 08:55 
References:  Engle, R., Granger, C. (1987). Cointegration and error correction: representation, estimation, and testing. Journal of Econometrics, 55, 251276 Granger, C., Newbold, P. (1967). Spurious regression in econometrics. Journal of Econometrics, 2, 111120 Hendry, D., Juselius, K. (2001). Explaining Cointegration Analysis: Part II. Energy Journal, 22, 75120 Johansen, S. (1988). Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control, 12, 231254 Kitov, I.O. (2006a). GDP growth rate and population, Working Papers 42, ECINEQ, Society for the Study of Economic Inequality. www.ecineq.org/milano/WP/ECINEQ200642.pdf Kitov, I.O., (2006b). Real GDP per capita in developed countries, MPRA Paper 2738, University Library of Munich, Germany. http://mpra.ub.unimuenchen.de/2738/01/MPRA_paper_2738.pdf Kitov, I.O., Kitov, O.I., Dolinskaya, S., (2007). Modelling real GDP per capita in the USA: cointegration test, MPRA Paper 2739, University Library of Munich, Germany. http://mpra.ub.unimuenchen.de/2739/01/MPRA_paper_2739.pdf U.S. Census Bureau. (2006a). Methodology. United States Population Estimates by Age, Sex, Race, and Hispanic Origin Method: July 1, 2006. Retrieved February 26, 2007 from http://www.census.gov/popest/topics/methodology/2006_nat_meth.html U.S. Census Bureau. (2006b). National intercensal estimates (19902000). Retrieved February 26, 2007 from http://www.census.gov/popest/archives/methodology/ intercensal_nat_meth.html 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/6056 