10/26/2005
Submission to the Ministry of Non-Predictive Studies, from Philip J. McDonnell

Periodically one market guru or another claims to have discovered a cycle in stock market prices. Some swear they exist and have developed elaborate mathematical machinery involving sums of complex exponential functions or folded sums of trigonometric functions. Because few people really understand these functions they have remained in the arcane realm of the mathematically enlightened. Others swear they have no validity and argue that the random walk is alive and well.

One recent claim on this forum has it that a 48 month cycle is alive and well in the market. One apocryphal story has it that the discovery was made while reading a chart upside down. Whether that story is true or not, an Australian market guru did claim the discovery.

The interesting thing about cycles is that they recur. If a perfectly regular 12 month cycle exists then what the market did 12 months ago it will do again this month. It recurs every 12 months. Thus a simple autocorrelation with a 12 month lag will show whether a 12-month cycle exists.

To this end all of the sSamp;P 500 index monthly percent changes were examined for the most recent available 500 months. The lags ranged from 1 month to 145 months (12+ years). The period covered was roughly 1950 to the present. Each autocorrelation was based on 500 observations. For n=500 a significant correlation would be 8.8% or better.

Out of the 145 correlations only 6 were found to rise to the level of 5% significance. However for 145 such calculations we would have expected 5% or 7 of them to be significant simply by chance. Thus the 6 found are quite consistent with randomness and offer no support for the idea that monthly cycles run rampant in the data.

Here are the correlations for the obvious suspects:

Months      Correlation
  3            1.52%
 12            3.82
 24            1.56
 48           -1.76
120            1.49

Note that the purported 48-month cycle is insignificant and it is the wrong sign! (*) There were no significant correlations in the 15 month interval within 7 months plus or minus. One notes that 5% significance is a 1 in 20 chance. So with 15 chances out of 20 one would expect a significant result about 3 times out of 4 simply due to chance. Thus the results did not even rise to the level of randomness.

It appears that the principle of ever changing cycles eliminated most of the monthly cycles long ago.

Philip J. McDonnell

(*) The wrong sign may be a data artifact, caused by reading chart books upside down.

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