Frequency Analysis based on Monthly Comb
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Short term fluctuations that seem to repeat with a regular frequency are often (even generally) seen in stock price charts. 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, attempts to exploit the market cycles are foiled by the deviation from strictly periodic behavior required by ordinary analysis. 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) = 25.00
Sawtooth = 48.28
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 17.53 | 32.00 | 25.00 | 9.68 % | | Low | 17.16 | 32.00 | 24.00 | 9.36 % |
| Recent High | Price | Recent Low | Price | Cycle | | Wednesday, February 03, 2010 | 64.66 | | | 25 | | | Wednesday, January 06, 2010 | 60.93 | 18 | | Monday, December 28, 2009 | 63.07 | | | 28 | | | Wednesday, December 09, 2009 | 60.09 | 61 | | Monday, November 16, 2009 | 63.44 | | | 56 | | | Monday, September 14, 2009 | 53.31 | 19 | | Thursday, August 27, 2009 | 55.70 | | | 26 | | | Monday, August 17, 2009 | 53.11 | 37 |
Fourier Transform after Digital Filter M | Cycle Length | Fourier Amplitude | | 13 | 0.52 | | 20 | 0.37 | | 17 | 0.33 | | 25 | 0.30 | | 29 | 0.29 | | 32 | 0.27 | | 36 | 0.16 | | 39 | 0.14 | | 59 | 0.13 | | 53 | 0.13 | | 44 | 0.12 |
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Frequency Analysis based on Quarterly Comb
Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 62.00
Sawtooth = 46.15
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 51.94 | 91.00 | 62.00 | 16.83 % | | Low | 47.92 | 91.00 | 66.00 | 11.98 % |
| Recent High | Price | Recent Low | Price | Cycle | | Monday, November 16, 2009 | 63.44 | | | 116 | | | Monday, August 17, 2009 | 53.11 | 74 | | Wednesday, June 03, 2009 | 58.95 | | | 104 | | | Friday, May 01, 2009 | 50.65 | 40 | | | Thursday, March 05, 2009 | 49.16 | 96 | | Friday, January 02, 2009 | 61.05 | | | 100 | | | Wednesday, October 15, 2008 | 48.93 | 75 | | Monday, August 11, 2008 | 62.22 | | | 62 |
Fourier Transform after Digital Filter Q | Cycle Length | Fourier Amplitude | | 13 | 0.31 | | 21 | 0.21 | | 17 | 0.19 | | 25 | 0.17 | | 158 | 0.16 | | 27 | 0.15 | | 29 | 0.15 | | 273 | 0.14 | | 195 | 0.14 | | 87 | 0.13 | | 33 | 0.13 |
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Frequency Analysis based on Yearly Comb
Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 44.50
| 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, October 15, 2008 | 48.93 | 590 | | Monday, August 11, 2008 | 62.22 | | | 167 | | Tuesday, December 11, 2007 | 58.77 | | | 459 | | | Tuesday, June 13, 2006 | 28.28 | 236 | | Tuesday, February 14, 2006 | 32.21 | | | 490 | | | Wednesday, July 06, 2005 | 24.04 | 584 | | Friday, March 05, 2004 | 25.43 | | | 450 | | | Wednesday, March 12, 2003 | 10.39 | 491 |
Fourier Transform on Raw Closing Prices | Cycle Length | Fourier Amplitude | | 819 | 3.32 | | 683 | 3.09 | | 512 | 2.46 | | 315 | 2.04 | | 372 | 1.98 | | 455 | 1.77 | | 12 | 1.76 | | 585 | 1.75 | | 241 | 1.33 | | 16 | 1.24 | | 195 | 1.17 |
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| Breaking News: Friday, March 19, 2010: We have news on AT and T, ticker symbol T. A significant moving average event has happened.
Also, there are breaking events concerning L-3 Communications Holdings, Inc. and Electronic Data Systems.
From the News Archive: (3/18/2010 ) Bad news came from Mylan Inc., TECO Energy, Inc., MicroSoft, and Goldman Sachs Group, 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 - 7 instances | | | | Future30SesAvgClose | 1.23 % minus 1.96 % = -0.74 % | -6.23 % | | Future5SesAvgClose | 0.32 % minus 0.42 % = -0.11 % | -5.35 % | | Future2SesAvgClose | 0.14 % minus 0.22 % = -0.08 % | -10.16 % | | Sell Signals - 5 instances | | Future30SesAvgClose | 13.35 % minus 1.96 % = 11.39 % | 96.43 % | | Future5SesAvgClose | 0.52 % minus 0.42 % = 0.10 % | 5.03 % | | Future2SesAvgClose | -0.19 % minus 0.22 % = -0.41 % | -51.74 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 55 instances | | | | Future30SesAvgClose | 0.63 % minus 1.96 % = -1.33 % | -11.26 % | | Future5SesAvgClose | 0.16 % minus 0.42 % = -0.26 % | -13.39 % | | Future2SesAvgClose | 0.04 % minus 0.22 % = -0.18 % | -22.77 % | | Sell Signals - 53 instances | | Future30SesAvgClose | 1.68 % minus 1.96 % = -0.28 % | -2.38 % | | Future5SesAvgClose | -0.19 % minus 0.42 % = -0.61 % | -31.08 % | | Future2SesAvgClose | -0.29 % minus 0.22 % = -0.51 % | -64.38 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30 | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 18 instances | | | | Future30SesAvgClose | 0.98 % minus 1.96 % = -0.99 % | -8.36 % | | Future5SesAvgClose | 0.66 % minus 0.42 % = 0.24 % | 12.19 % | | Future2SesAvgClose | 0.46 % minus 0.22 % = 0.24 % | 30.33 % | | Sell Signals - 5 instances | | Future30SesAvgClose | 5.62 % minus 1.96 % = 3.66 % | 31.00 % | | Future5SesAvgClose | 2.53 % minus 0.42 % = 2.11 % | 107.08 % | | Future2SesAvgClose | 1.39 % minus 0.22 % = 1.17 % | 148.87 % | | . | | | Projection of Representative Monthly Cycle | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 217 instances | | | | Future30SesAvgClose | 1.07 % minus 1.96 % = -0.89 % | -7.56 % | | Future5SesAvgClose | 0.23 % minus 0.42 % = -0.20 % | -10.10 % | | Future2SesAvgClose | 0.18 % minus 0.22 % = -0.04 % | -4.65 % | | Sell Signals - 230 instances | | Future30SesAvgClose | 1.61 % minus 1.96 % = -0.35 % | -2.99 % | | Future5SesAvgClose | 0.31 % minus 0.42 % = -0.11 % | -5.76 % | | Future2SesAvgClose | 0.08 % minus 0.22 % = -0.13 % | -17.10 % | | . | | | Projection of BiWeekly Modal Cycles | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 463 instances | | | | Future30SesAvgClose | 1.69 % minus 1.96 % = -0.28 % | -2.35 % | | Future5SesAvgClose | 0.31 % minus 0.42 % = -0.12 % | -5.90 % | | Future2SesAvgClose | 0.08 % minus 0.22 % = -0.13 % | -16.97 % | | Sell Signals - 463 instances | | Future30SesAvgClose | 1.30 % minus 1.96 % = -0.67 % | -5.64 % | | Future5SesAvgClose | 0.21 % minus 0.42 % = -0.21 % | -10.91 % | | Future2SesAvgClose | 0.09 % minus 0.22 % = -0.12 % | -15.70 % | | . | | | | |
| The best buy signal for 30 future sessions was -0.28 % from the Projection of BiWeekly Modal Cycles,and the best sell signal for was -0.67 % from the Projection of BiWeekly Modal Cycles. | | For 5 future sessions the best buy signal was 0.24 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.61 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing. | | The best buy signal for 2 future sessions was 0.24 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.51 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing. |
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