Long-Term Approximation by Spectral Analysis

The approximation of the S&P 500 from Jan 3, 1950 to Nov. 28, 2014

via spectral analysis

The 66-year approximation of the S&P 500 was updated on Dec. 4, 2014

due to the improvement in the spectral analysis I had developed for

the investigation of random motion.

The approximation of the NY Dow from Jan. 2, 1918 to Nov. 28, 2014 via spectral analysis.

The New York Dow went below -2σ only twice, during the Great Depression in 1930s and during

the Great Recession of 2007-2009. The spectral analysis surely captures the gravity of these crises.