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, a fact that has played havoc with most schemes to exploit the market 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) = 31.00 Sawtooth = 49.84
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 16.58 | 31.00 | 29.00 | 14.82 % | | Low | 16.29 | 31.00 | 15.00 | 18.21 % |
| Recent High | Price | Recent Low | Price | Cycle | | Tuesday, November 04, 2008 | 19.99 | | | 32 | | | Thursday, October 09, 2008 | 13.32 | 19 | | Friday, September 19, 2008 | 29.50 | | | 14 | | | Friday, September 12, 2008 | 17.05 | 17 | | Friday, August 29, 2008 | 27.89 | | | 28 | | | Tuesday, August 19, 2008 | 23.43 | 16 | | | Monday, July 28, 2008 | 23.93 | 84 | | Tuesday, July 22, 2008 | 33.62 | | | 55 |
Fourier Transform after Digital Filter M | Cycle Length | Fourier Amplitude | | 9 | 0.78 | | 14 | 0.53 | | 16 | 0.49 | | 20 | 0.32 | | 23 | 0.31 | | 26 | 0.28 | | 32 | 0.22 | | 29 | 0.21 | | 35 | 0.16 | | 41 | 0.16 | | 39 | 0.13 |
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Frequency Analysis based on Quarterly Comb
Frequency from Quarterly Comb Filter Representative Cycle (Trading Sessions) = 97.00 Sawtooth = 50.71
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 48.06 | 88.00 | 70.00 | 27.19 % | | Low | 50.14 | 84.00 | 62.00 | 24.11 % |
| Recent High | Price | Recent Low | Price | Cycle | | Friday, September 19, 2008 | 29.50 | | | 97 | | | Friday, March 28, 2008 | 38.86 | 55 | | Friday, May 02, 2008 | 51.30 | | | 63 | | | Tuesday, January 08, 2008 | 46.47 | 100 | | Friday, February 01, 2008 | 56.34 | | | 81 | | | Wednesday, August 15, 2007 | 65.68 | 107 | | Friday, October 05, 2007 | 73.45 | | | 97 | | | Wednesday, March 14, 2007 | 75.14 | 187 |
Fourier Transform after Digital Filter Q | Cycle Length | Fourier Amplitude | | 16 | 0.26 | | 205 | 0.17 | | 178 | 0.16 | | 20 | 0.15 | | 49 | 0.14 | | 85 | 0.13 | | 24 | 0.13 | | 164 | 0.13 | | 26 | 0.13 | | 41 | 0.13 | | 53 | 0.12 |
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Frequency Analysis based on Yearly Comb
Representative Cycle (Trading Sessions) = 0.00 Sawtooth = 46.94
| 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 | | Wednesday, January 24, 2007 | 92.05 | | | 202 | | | Wednesday, June 14, 2006 | 61.73 | 467 | | Tuesday, April 04, 2006 | 75.81 | | | 273 | | | Friday, August 06, 2004 | 44.86 | 461 | | Friday, March 04, 2005 | 58.09 | | | 251 | | | Monday, October 07, 2002 | 26.83 | 262 | | Friday, March 05, 2004 | 60.64 | | | 540 | | | Thursday, September 20, 2001 | 33.99 | 525 |
Fourier Transform on Raw Closing Prices | Cycle Length | Fourier Amplitude | | 819 | 10.85 | | 585 | 6.12 | | 455 | 5.50 | | 683 | 4.93 | | 241 | 4.05 | | 12 | 3.74 | | 410 | 3.71 | | 273 | 3.69 | | 293 | 3.49 | | 178 | 3.11 | | 17 | 2.73 |
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| Breaking News: Friday, March 19, 2010: We have news on L-3 Communications Holdings, Inc., ticker symbol LLL. Signs of an over-bought condition have become noticable.
Also, there are breaking events concerning American Tower Corporation and TECO Energy, Inc..
From the News Archive: (3/18/2010 ) Bad news came from Allergan, Inc., Sempra Energy, MicroSoft, and Mylan Inc..
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Average Sawtooth based on Monthly Combo
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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. The Sawtooth Statistic gives a clue to the general mood of the markets, functioning as a sort of sentiment indicator. 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 - 3 instances | | | | Future30SesAvgClose | 11.82 % minus 2.73 % = 9.08 % | 76.89 % | | Future5SesAvgClose | 4.72 % minus 0.55 % = 4.17 % | 211.87 % | | Future2SesAvgClose | 1.56 % minus 0.28 % = 1.28 % | 162.65 % | | Sell Signals - 6 instances | | Future30SesAvgClose | 3.62 % minus 2.73 % = 0.88 % | 7.47 % | | Future5SesAvgClose | -0.02 % minus 0.55 % = -0.57 % | -29.06 % | | Future2SesAvgClose | -0.15 % minus 0.28 % = -0.43 % | -54.61 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 48 instances | | | | Future30SesAvgClose | 1.68 % minus 2.73 % = -1.05 % | -8.93 % | | Future5SesAvgClose | 0.22 % minus 0.55 % = -0.33 % | -16.90 % | | Future2SesAvgClose | -0.01 % minus 0.28 % = -0.29 % | -36.57 % | | Sell Signals - 49 instances | | Future30SesAvgClose | 2.82 % minus 2.73 % = 0.09 % | 0.73 % | | Future5SesAvgClose | 0.18 % minus 0.55 % = -0.37 % | -19.03 % | | Future2SesAvgClose | 0.31 % minus 0.28 % = 0.03 % | 3.24 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30 | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 11 instances | | | | Future30SesAvgClose | 4.90 % minus 2.73 % = 2.17 % | 18.37 % | | Future5SesAvgClose | 1.35 % minus 0.55 % = 0.80 % | 40.64 % | | Future2SesAvgClose | 0.13 % minus 0.28 % = -0.15 % | -18.91 % | | Sell Signals - 16 instances | | Future30SesAvgClose | 7.87 % minus 2.73 % = 5.14 % | 43.51 % | | Future5SesAvgClose | 1.02 % minus 0.55 % = 0.47 % | 24.03 % | | Future2SesAvgClose | 0.27 % minus 0.28 % = -0.02 % | -2.13 % | | . | | | Projection of Representative Monthly Cycle | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 170 instances | | | | Future30SesAvgClose | 1.89 % minus 2.73 % = -0.84 % | -7.12 % | | Future5SesAvgClose | 0.26 % minus 0.55 % = -0.29 % | -14.83 % | | Future2SesAvgClose | 0.14 % minus 0.28 % = -0.14 % | -17.85 % | | Sell Signals - 183 instances | | Future30SesAvgClose | 2.93 % minus 2.73 % = 0.20 % | 1.66 % | | Future5SesAvgClose | 0.78 % minus 0.55 % = 0.23 % | 11.82 % | | Future2SesAvgClose | 0.48 % minus 0.28 % = 0.20 % | 25.37 % | | . | | | Projection of BiWeekly Modal Cycles | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 376 instances | | | | Future30SesAvgClose | 2.85 % minus 2.73 % = 0.11 % | 0.96 % | | Future5SesAvgClose | 0.66 % minus 0.55 % = 0.10 % | 5.31 % | | Future2SesAvgClose | 0.31 % minus 0.28 % = 0.03 % | 3.24 % | | Sell Signals - 384 instances | | Future30SesAvgClose | 2.32 % minus 2.73 % = -0.41 % | -3.47 % | | Future5SesAvgClose | 0.49 % minus 0.55 % = -0.06 % | -3.24 % | | Future2SesAvgClose | 0.19 % minus 0.28 % = -0.09 % | -11.95 % | | . | | | | |
| The best buy signal for 30 future sessions was 9.08 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25,and the best sell signal for was -0.41 % from the Projection of BiWeekly Modal Cycles. | | For 5 future sessions the best buy signal was 4.17 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25,and the best sell signal was -0.57 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. | | The best buy signal for 2 future sessions was 1.28 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25,and the best sell signal was -0.43 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. |
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