Frequency Analysis based on Monthly Comb
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It is obvious from inspection of price lines, that many seem to contain cycles that may persist in repeating for a long time. Through the years, technicians have expended much effort to measure and exploit these cycles. It would appear simple enough to do a frequency analysis on the time series. But the cycles or periods that seem so easy to see in the price data, have proven to be surprisingly difficult to measure by classical methods. The classical methods apply to stationary cycles of exactly regular period. We can easily remove the trends from historical price data to make the series stationary. However, the fluctuations seen in financial data are almost never exactly periodic, complicating most attempts to take advantage of these cycles. One factor in the behaviour of market fluctuations is "Anticipation". When speculators detect a cycle in prices, they will buy earlier before the peak, and sell earlier before the dip. This phenomena causes an increase in frequency, and eventually a breakup of the established cycle. Traditional frequency analysis methods such as the Fourier Transform, break down badly attempting to deal with these irregularities. Wilder estimated that there was an important period of about 28 trading sessions. The half cycle of this period (14 sessions) is a default factor in many of the technical indicators. We have found this to be a reasonable figure, even in today's markets, but there is significant variation between issues. Some companies just seem to have faster or slower cycles for one reason or another, and the indicators may be more accurate when fitted to the situation. New methods had to be invented to deal with the seeming mathematical absurdity in the notion of non-periodic cycles. |
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Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 36.00
Sawtooth = 50.65
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 16.27 | 27.00 | 14.00 | 15.31 % | | Low | 17.19 | 30.00 | 24.00 | 14.90 % |
| Recent High | Price | Recent Low | Price | Cycle | | | Tuesday, August 31, 2010 | 39.60 | 41 | | Thursday, August 05, 2010 | 44.37 | | | 36 | | | Friday, July 02, 2010 | 33.97 | 19 | | Tuesday, June 15, 2010 | 39.00 | | | 23 | | | Monday, June 07, 2010 | 35.95 | 42 | | Wednesday, May 12, 2010 | 42.16 | | | 37 | | | Wednesday, April 07, 2010 | 36.33 | 36 | | Friday, March 19, 2010 | 38.40 | | | 40 |
Fourier Transform after Digital Filter M | Cycle Length | Fourier Amplitude | | 10 | 0.69 | | 18 | 0.54 | | 20 | 0.42 | | 25 | 0.38 | | 33 | 0.21 | | 29 | 0.19 | | 37 | 0.17 | | 41 | 0.16 | | 49 | 0.11 | | 55 | 0.11 | | 43 | 0.10 |
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Frequency Analysis based on Quarterly Comb
Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 87.00
Sawtooth = 47.83
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 48.24 | 76.00 | 38.00 | 20.42 % | | Low | 49.92 | 87.00 | 49.00 | 18.53 % |
| Recent High | Price | Recent Low | Price | Cycle | | | Friday, July 02, 2010 | 33.97 | 97 | | Wednesday, May 12, 2010 | 42.16 | | | 91 | | | Friday, February 12, 2010 | 32.69 | 68 | | Wednesday, December 30, 2009 | 35.23 | | | 71 | | | Wednesday, November 04, 2009 | 31.14 | 81 | | Friday, September 18, 2009 | 36.59 | | | 96 | | | Monday, July 13, 2009 | 29.55 | 87 | | Monday, May 04, 2009 | 36.52 | | | 123 |
Fourier Transform after Digital Filter Q | Cycle Length | Fourier Amplitude | | 10 | 0.38 | | 18 | 0.26 | | 20 | 0.22 | | 25 | 0.20 | | 132 | 0.16 | | 34 | 0.15 | | 37 | 0.14 | | 186 | 0.13 | | 31 | 0.13 | | 100 | 0.12 | | 82 | 0.12 |
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Frequency Analysis based on Yearly Comb
Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 0.00
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 0.00 | 0.00 | 0.00 | 0.00 % | | Low | 0.00 | 0.00 | 0.00 | 0.00 % |
| Recent High | Price | Recent Low | Price | Cycle | | | Monday, March 09, 2009 | 23.61 | 963 | | Tuesday, November 06, 2007 | 51.83 | | | 339 | | Monday, July 03, 2006 | 56.31 | | | 420 | | | Tuesday, May 10, 2005 | 22.89 | 690 | | Monday, November 01, 2004 | 27.62 | | | 866 | | | Tuesday, August 13, 2002 | 12.05 | 224 | | | Thursday, September 20, 2001 | 10.22 | 737 | | Thursday, May 17, 2001 | 15.40 | | | 901 |
Fourier Transform on Raw Closing Prices | Cycle Length | Fourier Amplitude | | 819 | 3.54 | | 512 | 2.68 | | 683 | 2.25 | | 455 | 2.24 | | 585 | 1.99 | | 341 | 1.63 | | 14 | 1.53 | | 372 | 1.33 | | 273 | 1.31 | | 16 | 1.21 | | 20 | 1.21 |
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| EXPD
Expeditors International of Washington
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Average Sawtooth based on Monthly Combo
| EXPD
Expeditors International of Washington
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Average Sawtooth based on Bi-weekly Combo
The Sawtooth statistic measures the time from each periodic high to the next periodic low, in comparison to the time from that low to the next high point . The mid-point, corresponding to a perfect sine wave, is 50 percent. Values less than this indicate the sell slope is steeper than the buy slope, while values over 50 percent show the opposite. This is supposed to indicate the degree of fear or greed. The chart represents the sawtooth percentage of (approximately) monthly cycles over the past year, and of the (approximately) bi-weekly cycles, averaged over the past six months.
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