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The Professor
Charles Pennington

01/29/2005
Moon-Gazing with Professor Pennington

Recently the Spec-List started pondering the moon, and whether it affects markets, and then it spilled over into the Hebrew calendar, bass fishing, and other subjects. Even outside of the Spec-List there have been speculations that markets go up and down with the phases of the moon. Some commodity trading books have proposed there is lunar cyclicality in soybean futures, silver, and other things. Here I only test the S&P.

Fortunately, this is something that can be tested using the dreaded method of FOURIER ANALYSIS (caps courtesy of Mr. E). This is something that I used to use every day when I was a professor doing nuclear magnetic resonance spectroscopy ("NMR") and magnetic resonance imaging ("MRI").

Fourier analysis is a big, long subject, with many possibilities for the conventions that are used, etc., and I want to avoid delving into that. The point though is that it tells you how much "stuff" you have at each frequency. If data has a lot of periodicity to it at a period of 28 calendar days, then that will show up as a "peak" in the Fourier transform at a frequency corresponding to (1 divided by 28 calendar days).

1) I took the last 2048 closing prices of SPY, Fourier transformed them, and plotted the magnitude of the Fourier transform. (It has complex numbers, and the magnitude is the square root of the real part squared plus the imaginary part squared.)

2) I then took the 2048 closing prices and ARTIFICIALLY added a cosine wave with an amplitude of $1 and a period of 28 calendar days. Then I Fourier transformed THAT, and took the magnitude.

The reason that I did item 2 is that using that Fourier transform, you can see how big the peak would be IF the moon made SPY go up and down by an extra $1 with a period of 28 days.

The Fourier transforms for items 1) and 2) are both shown in the attached gif file.

You will see in item 2 that the artificially added $1 cosine wave of period 28 days shows up as a peak in the Fourier transform that's much bigger than the background noise. (The background isn't necessarily "noise", but anyway...)

But in item 1, which is the data for SPY with nothing artificially added, you see no peak at that frequency.

The conclusion is that if there's anything periodic in SPY with frequency near 28 calendar days, it's got to have an amplitude of much less than $1.

Charles Pennington trades stocks and stock index futures with Victor Niederhoffer's Manchester Trading in Weston, Connecticut. Before becoming a hedge fund trader Charles was a Full Professor of Physics at Ohio State University, where he taught for 13 years and served as advisor to eight successful doctoral candidates. He has published more than 40 scientific papers and won a Presidential Young Investigator grant (1993-1998). He earned his B.S. (1985) and Ph.D. degrees (1989) in Physics from the University of North Carolina at Chapel Hill and the University of Illinois at Urbana-Champaign, respectively.