**Some Background**

J M Hurst referred to nominal cycles of 40, 20, 10 and 5 days in share prices. To this day many people use 5 and 20 day moving averages based on his findings. He used other longer cycles also and his cycles were all harmonically related by ratios of 1:2 and 1:3. Edward Dewey also mentioned many cycles related by 1:2 and 1:3 ratios, but generally with somewhat longer periods. I have been told that W D Gann also referred to “degrees” which referred to cycles of days that relate to these periods.

**Initial Analysis**

This analysis uses the daily adjusted close prices for International Business Machines shares from 1962/01/02 to 2010/06/18 obtained from Yahoo!, see http://biz.yahoo.com/p/i/ibm.html

Using CATS, the logs of prices were first calculated and then a spectrum was determined. In order of importance, the most significant (judged by Bartel’s test) cycles periods in days were determined accurately and found to be:

13.04444, 20.97479, 39.25047, 264.97006, 9.96358, 6.99862, 6.78632, 9.01824, 19.89972, 486.93262, 3.04275, 20.01583, 11.38388, 19.55628, 9.83656, 18.9238, 5.38226, 7.00244, 6.77017, 9.51347, 11.23574, 66.90607, 4.30886, 10.74792, 9.2492, 27.22281, 4.41162, 21.37294, 18.11798, 5583.59619, 29.362, 3.1256, 55.85006, 17.10095, 4.5914, 22.57135, 17.40327, 7.30831, 10.69823, 10.50707, 37.66518, 9.6833, 24.27218, 25.77207, 10.80006, 9.31388, 8.05267, 5.01381, 8.71767, 8.2742, 20.92842, 15.10677, 4.26676, 10.67899, 29.82359, 136.41618, 9.23737, 5.01661, 25.42738, 16.70852, 19.41513, 24.86968, 14.61892, 5.68271, 7.90454, 10.55538, 91.45869

These 67 periods were then used in the next part of the analysis.

**Communalities of Cycles Periods**

Kotov’s method for finding communalities amoung these periods was then used. In essence this method looks for new values that are related by near to integer ratios to the whole list of values. So in the following graph, a peak means that at that “period” there is a maximum communality, or minimum sum of differences from integer ratios.

In the range from 1 day to 150 days, there are six periods at which there are large peaks in the communality. These periods are all near to being at simple harmonic ratio from each other. The peaks, as indicated, are near to periods of 120 – 60 – 20 – 10 – 5 – 2.5 days. These periods are all related by 2:1 ratios except one which is by 3:1 ratio. Furthermore, the periods do accord with Hursts periods as used in his methods of stock trading.

This is a very clear confirmation of real cycles matching the patterns of ratios attested to by Dewey and Hurst. It can be stated clearly that real cycles in IBM share price tend to be related by simple whole number ratios to specific periods near to the above set of periods.

Hi Ray,

great interesting study !

Are the number of days shown in the results Trading days or Calendar Days ?

Best regards. Alain fom Paris

Hi Alain

Thanks. Good question, thank you. The cycles periods are all in calendar days.

Now that I think about it, the 5 and 20 day moving averages are normally trading days aren’t they? That would make them 7 and 28 calendar days.

In other studies as well as this one, there is evidence for cycles of 28, 14, 7 and 3.5 calendar days. These appear in many geomagnetic cycles and solar phenomena – the Sun’s rotation period is 28 days after all (as seen from the Earth) and its magnetic field structure naturally leads to divisions by two. We do find 7.0, 10.5 and 21.0 day cycles in the individual ones above.

Regards

Ray

Ray,

thank you for the answer.

I think it is always necessary, when speaking about “cycles” in market data to precise if we use Trading or Calendar days for daily data. Years are Years, Months are months, Weeks are already more debatable (what about the week end pause ?)

In my opinion cycles in the market are “man made”.

Natural cycles weather, astronomy, whatever, work obviously round the clock, but for me when the bell rings cycle influence stops !

Regards Alain

Ray,

I agree with you about the Moving Averages. They are based on Trading Days.

I think that coherence is necessary. If my data are in Trading days, my moving averages have to be in Trading Days, my Cycles too ! and conversely for Calendar Days.

Alain

Hi Alain

This analysis was done with CATS. We started off in CATS intending to have trading days as a distinct category separate from days, weeks, months etc. and then a variety of things caused us to rethink that. They were:

1. Old DJIA data had 6 day working week.

2. Missing data sometimes for holidays.

3. We disagreed with you and think that cycles run around the clock. 🙂

4. We wanted to be able to synchronize our data between market cycles and scientific cycles and to therefore mix trading day and daily data.

So we hit on the idea of using missing data as a way to cope with omitted trading days (usually Saturday and Sunday, but also holidays, and Saturday not missing before about 1940s). This means that we run all our cycles 24 hours a day, 7 days a week, and only ever determine cycles in days, never trading days. So any CATS based reports you see here will normally adhere to that.

CATS allows missing data to be treated in 3 ways: replace by zero, replace by previous value, and interpolate. For market trading, the previous value is a more pure way to determine what happens as it is still the “latest close”. For cycles analysis the interpolation is probably the best guess, but care must be taken in not thinking you can predict that well, because Saturday data is based in part on unknown Monday data.

Of course you will get very similar results using trading day cycles and multiplying the periods by 1.4 to get calendar days. Especially for longer cycles the difference is likely to be negligible. However for a 2.5 day cycle (if such a thing exists) that runs around the clock, the difference may be very noticeable as with 5 days of data there will be almost a complete missing cycle each week. That means that a true, around the clock 2.5 day cycle will appear in our method as having 2.8 cycles per week, but in trading data will likely be detected as having just 1.8 cycles per week (this problem is related to the problem known as “aliasing”) or seen as a 3.89 day cycle.

However, if you are right, and these cycles are totally man made and stop when markets close, then the above paragraph will be irrelevant. This is another whole subject, and worthy of detailed investigation. Preliminary work indicates that cycles do run all the time. Let us have a contest to find some proof on this one way or the other!