Frequency Analysis based on Monthly Comb
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Even a casual examination of historical price lines seems to reveal cycles or regular short term fluctuations that continue repeating. 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) = 32.00
Sawtooth = 48.14
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 16.82 | 32.00 | 27.00 | 10.29 % | | Low | 16.64 | 32.00 | 29.00 | 9.20 % |
| Recent High | Price | Recent Low | Price | Cycle | | Friday, September 24, 2010 | 37.34 | | | 32 | | | Friday, August 20, 2010 | 34.08 | 15 | | Tuesday, August 10, 2010 | 35.40 | | | 18 | | | Friday, July 30, 2010 | 34.10 | 19 | | Thursday, July 15, 2010 | 36.11 | | | 21 | | | Friday, July 02, 2010 | 33.87 | 30 | | Tuesday, June 15, 2010 | 35.65 | | | 58 | | | Thursday, May 20, 2010 | 31.14 | 69 |
Fourier Transform after Digital Filter M | Cycle Length | Fourier Amplitude | | 16 | 0.42 | | 20 | 0.39 | | 18 | 0.38 | | 23 | 0.34 | | 25 | 0.29 | | 28 | 0.26 | | 30 | 0.24 | | 34 | 0.20 | | 41 | 0.20 | | 36 | 0.18 | | 55 | 0.14 |
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Frequency Analysis based on Quarterly Comb
Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 43.00
Sawtooth = 48.51
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 47.43 | 83.00 | 43.00 | 14.58 % | | Low | 46.74 | 86.00 | 52.00 | 13.76 % |
| Recent High | Price | Recent Low | Price | Cycle | | | Friday, August 20, 2010 | 34.08 | 64 | | Thursday, July 15, 2010 | 36.11 | | | 79 | | | Thursday, May 20, 2010 | 31.14 | 69 | | Tuesday, March 23, 2010 | 37.68 | | | 43 | | | Wednesday, February 10, 2010 | 35.06 | 67 | | Wednesday, January 20, 2010 | 39.74 | | | 263 | | | Tuesday, November 03, 2009 | 29.41 | 167 | | Friday, January 02, 2009 | 28.49 | | | 268 |
Fourier Transform after Digital Filter Q | Cycle Length | Fourier Amplitude | | 10 | 0.42 | | 14 | 0.22 | | 20 | 0.21 | | 16 | 0.21 | | 85 | 0.17 | | 23 | 0.16 | | 102 | 0.15 | | 25 | 0.15 | | 33 | 0.13 | | 146 | 0.13 | | 27 | 0.13 |
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Frequency Analysis based on Yearly Comb
Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 50.34
| 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 20, 2010 | 39.74 | | | 531 | | | Monday, March 09, 2009 | 19.61 | 858 | | Monday, December 10, 2007 | 53.44 | | | 655 | | | Friday, October 07, 2005 | 20.92 | 230 | | Wednesday, May 04, 2005 | 27.56 | | | 228 | | | Tuesday, November 09, 2004 | 20.00 | 238 | | Tuesday, June 08, 2004 | 36.89 | | | 245 | | | Friday, November 28, 2003 | 30.23 | 342 |
Fourier Transform on Raw Closing Prices | Cycle Length | Fourier Amplitude | | 819 | 4.18 | | 585 | 3.32 | | 683 | 2.94 | | 455 | 1.85 | | 228 | 1.25 | | 512 | 1.17 | | 137 | 1.09 | | 15 | 1.04 | | 195 | 1.00 | | 293 | 1.00 | | 18 | 0.91 |
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| Breaking News: Friday, November 12, 2010: We have news on Cree, Inc., ticker symbol CREE. Signs of an over-bought condition have become noticable.
Also, there are breaking events concerning Intel and PetSmart, Inc.
From the News Archive: (11/11/2010 ) Favorable events happened at Exxon Mobil, Ingersoll-Rand Company Limited, and Concur Technologies, Inc.. Meanwhile, bad news came from International Game Technology.
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Merck
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Average Sawtooth based on Monthly Combo
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Merck
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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 - 8 instances | | | | Future30SesAvgClose | 2.65 % minus 2.04 % = 0.60 % | 5.09 % | | Future5SesAvgClose | 0.53 % minus 0.39 % = 0.14 % | 7.14 % | | Future2SesAvgClose | 0.02 % minus 0.19 % = -0.17 % | -21.65 % | | Sell Signals - 7 instances | | Future30SesAvgClose | -0.86 % minus 2.04 % = -2.90 % | -24.57 % | | Future5SesAvgClose | -1.36 % minus 0.39 % = -1.75 % | -89.03 % | | Future2SesAvgClose | -0.40 % minus 0.19 % = -0.60 % | -75.75 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 55 instances | | | | Future30SesAvgClose | 2.00 % minus 2.04 % = -0.04 % | -0.37 % | | Future5SesAvgClose | 0.58 % minus 0.39 % = 0.19 % | 9.62 % | | Future2SesAvgClose | 0.34 % minus 0.19 % = 0.14 % | 18.21 % | | Sell Signals - 54 instances | | Future30SesAvgClose | 0.77 % minus 2.04 % = -1.27 % | -10.76 % | | Future5SesAvgClose | -0.22 % minus 0.39 % = -0.61 % | -31.08 % | | Future2SesAvgClose | -0.12 % minus 0.19 % = -0.32 % | -40.19 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30 | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 13 instances | | | | Future30SesAvgClose | 2.34 % minus 2.04 % = 0.30 % | 2.52 % | | Future5SesAvgClose | 0.41 % minus 0.39 % = 0.02 % | 0.87 % | | Future2SesAvgClose | 0.21 % minus 0.19 % = 0.02 % | 2.59 % | | Sell Signals - 13 instances | | Future30SesAvgClose | 3.86 % minus 2.04 % = 1.82 % | 15.40 % | | Future5SesAvgClose | 0.95 % minus 0.39 % = 0.56 % | 28.34 % | | Future2SesAvgClose | 0.53 % minus 0.19 % = 0.33 % | 42.37 % | | . | | | Projection of Representative Monthly Cycle | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 217 instances | | | | Future30SesAvgClose | 1.68 % minus 2.04 % = -0.37 % | -3.10 % | | Future5SesAvgClose | 0.47 % minus 0.39 % = 0.08 % | 4.19 % | | Future2SesAvgClose | 0.25 % minus 0.19 % = 0.06 % | 7.57 % | | Sell Signals - 238 instances | | Future30SesAvgClose | 1.28 % minus 2.04 % = -0.76 % | -6.47 % | | Future5SesAvgClose | 0.22 % minus 0.39 % = -0.17 % | -8.54 % | | Future2SesAvgClose | 0.13 % minus 0.19 % = -0.06 % | -8.01 % | | . | | | Projection of BiWeekly Modal Cycles | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 492 instances | | | | Future30SesAvgClose | 1.25 % minus 2.04 % = -0.79 % | -6.69 % | | Future5SesAvgClose | 0.31 % minus 0.39 % = -0.08 % | -4.24 % | | Future2SesAvgClose | 0.14 % minus 0.19 % = -0.05 % | -6.66 % | | Sell Signals - 463 instances | | Future30SesAvgClose | 1.42 % minus 2.04 % = -0.63 % | -5.33 % | | Future5SesAvgClose | 0.28 % minus 0.39 % = -0.11 % | -5.46 % | | Future2SesAvgClose | 0.13 % minus 0.19 % = -0.06 % | -7.65 % | | . | | | | |
| The best buy signal for 30 future sessions was 0.60 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25,and the best sell signal for was -2.90 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. | | For 5 future sessions the best buy signal was 0.19 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing,and the best sell signal was -1.75 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. | | The best buy signal for 2 future sessions was 0.14 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing,and the best sell signal was -0.60 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. |
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