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. The paradoxical condition of variable length periods forces the adoptation of some new forms of analysis. |
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Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 21.00
Sawtooth = 52.67
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 17.38 | 31.00 | 21.00 | 26.87 % | | Low | 16.00 | 32.00 | 30.00 | 33.16 % |
| Recent High | Price | Recent Low | Price | Cycle | | Wednesday, October 05, 2005 | 3.05 | | | 15 | | | Tuesday, September 27, 2005 | 2.26 | 25 | | Wednesday, September 14, 2005 | 3.30 | | | 30 | | | Monday, August 22, 2005 | 2.71 | 33 | | Tuesday, August 02, 2005 | 3.88 | | | 24 | | | Wednesday, July 06, 2005 | 3.22 | 47 | | Tuesday, June 28, 2005 | 3.60 | | | 99 | | | Thursday, April 28, 2005 | 1.45 | 21 |
Fourier Transform after Digital Filter M | Cycle Length | Fourier Amplitude | | 18 | 0.33 | | 24 | 0.28 | | 28 | 0.25 | | 30 | 0.21 | | 32 | 0.21 | | 21 | 0.19 | | 37 | 0.17 | | 35 | 0.15 | | 51 | 0.13 | | 41 | 0.12 | | 39 | 0.12 |
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Frequency Analysis based on Quarterly Comb
Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 46.00
Sawtooth = 44.51
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 57.33 | 86.00 | 77.00 | 43.37 % | | Low | 45.00 | 82.00 | 46.00 | 33.37 % |
| Recent High | Price | Recent Low | Price | Cycle | | Tuesday, August 02, 2005 | 3.88 | | | 148 | | | Thursday, April 28, 2005 | 1.45 | 67 | | | Friday, January 21, 2005 | 3.13 | 68 | | Thursday, December 30, 2004 | 3.96 | | | 77 | | | Thursday, October 14, 2004 | 2.32 | 46 | | Friday, September 10, 2004 | 3.95 | | | 54 | | | Tuesday, August 10, 2004 | 3.25 | 58 | | Thursday, June 24, 2004 | 4.70 | | | 89 |
Fourier Transform after Digital Filter Q | Cycle Length | Fourier Amplitude | | 137 | 0.26 | | 12 | 0.20 | | 18 | 0.19 | | 186 | 0.19 | | 15 | 0.16 | | 102 | 0.15 | | 146 | 0.15 | | 28 | 0.14 | | 35 | 0.13 | | 24 | 0.12 | | 71 | 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 | | | Thursday, April 28, 2005 | 1.45 | 135 | | Tuesday, February 17, 2004 | 6.27 | | | 153 | | | Thursday, October 14, 2004 | 2.32 | 507 | | Wednesday, July 09, 2003 | 7.84 | | | 547 | | | Wednesday, October 09, 2002 | 1.66 | 434 | | Monday, April 30, 2001 | 56.99 | | | 909 | | | Thursday, January 11, 2001 | 29.50 | 753 | | Friday, September 19, 1997 | 2.87 | | | 254 |
Fourier Transform on Raw Closing Prices | Cycle Length | Fourier Amplitude | | 683 | 5.86 | | 512 | 2.53 | | 6 | 2.52 | | 137 | 1.28 | | 146 | 1.20 | | 228 | 1.10 | | 186 | 1.08 | | 12 | 1.07 | | 17 | 1.03 | | 205 | 1.03 | | 158 | 1.00 |
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| Breaking News: Wednesday, July 01, 2009: We have news on Public Service Enterprise Group Inc., ticker symbol PEG. Signs of an over-bought condition have become noticable.
Also, there are breaking events concerning The Travelers Companies, Inc. and Kellogg Company.
From the News Archive: (7/1/2009 ) Favorable events happened at Allegheny Energy, Inc., Bank of America Corporation, and American International Group, Inc.. Meanwhile, bad news came from Lexmark International, Inc..
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Average Sawtooth based on Monthly Combo
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Average Sawtooth based on Bi-weekly Combo
A comparison of the average distance (in time) from each periodic high to to next periodic low, against the distance to the following high point, yields the Sawtooth Statistic. 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.
| . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25 | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 0 instances | | | | Sell Signals - 2 instances | | Future30SesAvgClose | -1.13 % minus 2.15 % = -3.28 % | -27.78 % | | Future5SesAvgClose | -4.58 % minus 0.44 % = -5.02 % | -255.05 % | | Future2SesAvgClose | -1.48 % minus 0.22 % = -1.70 % | -216.39 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 18 instances | | | | Future30SesAvgClose | -3.27 % minus 2.15 % = -5.41 % | -45.82 % | | Future5SesAvgClose | -0.01 % minus 0.44 % = -0.45 % | -23.06 % | | Future2SesAvgClose | 0.41 % minus 0.22 % = 0.18 % | 23.30 % | | Sell Signals - 19 instances | | Future30SesAvgClose | 0.23 % minus 2.15 % = -1.92 % | -16.25 % | | Future5SesAvgClose | 0.08 % minus 0.44 % = -0.36 % | -18.27 % | | Future2SesAvgClose | 0.97 % minus 0.22 % = 0.74 % | 94.31 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30 | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 0 instances | | | | Sell Signals - 3 instances | | Future30SesAvgClose | 10.00 % minus 2.15 % = 7.86 % | 66.51 % | | Future5SesAvgClose | 0.57 % minus 0.44 % = 0.13 % | 6.62 % | | Future2SesAvgClose | 0.31 % minus 0.22 % = 0.09 % | 10.83 % | | . | | | Projection of Representative Monthly Cycle | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 54 instances | | | | Future30SesAvgClose | 0.71 % minus 2.15 % = -1.44 % | -12.20 % | | Future5SesAvgClose | -0.60 % minus 0.44 % = -1.04 % | -52.91 % | | Future2SesAvgClose | -0.82 % minus 0.22 % = -1.05 % | -133.05 % | | Sell Signals - 54 instances | | Future30SesAvgClose | 1.71 % minus 2.15 % = -0.44 % | -3.71 % | | Future5SesAvgClose | 0.65 % minus 0.44 % = 0.21 % | 10.70 % | | Future2SesAvgClose | 0.15 % minus 0.22 % = -0.08 % | -10.14 % | | . | | | Projection of BiWeekly Modal Cycles | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 116 instances | | | | Future30SesAvgClose | 2.88 % minus 2.15 % = 0.73 % | 6.17 % | | Future5SesAvgClose | 0.97 % minus 0.44 % = 0.53 % | 26.90 % | | Future2SesAvgClose | 0.25 % minus 0.22 % = 0.03 % | 3.51 % | | Sell Signals - 105 instances | | Future30SesAvgClose | 1.92 % minus 2.15 % = -0.22 % | -1.89 % | | Future5SesAvgClose | -0.02 % minus 0.44 % = -0.46 % | -23.48 % | | Future2SesAvgClose | -0.55 % minus 0.22 % = -0.78 % | -98.61 % | | . | | | | |
| The best buy signal for 30 future sessions was 0.73 % from the Projection of BiWeekly Modal Cycles,and the best sell signal for was -3.28 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. | | For 5 future sessions the best buy signal was 0.53 % from the Projection of BiWeekly Modal Cycles,and the best sell signal was -5.02 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. | | The best buy signal for 2 future sessions was 0.18 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing,and the best sell signal was -1.70 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. |
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