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, 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. 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) = 30.00
Sawtooth = 50.78
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 15.19 | 30.00 | 13.00 | 32.17 % | | Low | 17.00 | 30.00 | 27.00 | 39.86 % |
| Recent High | Price | Recent Low | Price | Cycle | | | Friday, January 29, 2010 | 25.42 | 42 | | Wednesday, January 06, 2010 | 31.43 | | | 35 | | | Friday, November 27, 2009 | 19.66 | 17 | | Friday, November 13, 2009 | 21.95 | | | 14 | | | Tuesday, November 03, 2009 | 20.31 | 22 | | Monday, October 26, 2009 | 24.01 | | | 25 | | | Friday, October 02, 2009 | 20.09 | 33 | | Monday, September 21, 2009 | 22.93 | | | 42 |
Fourier Transform after Digital Filter M | Cycle Length | Fourier Amplitude | | 14 | 0.41 | | 11 | 0.39 | | 20 | 0.31 | | 18 | 0.31 | | 27 | 0.27 | | 37 | 0.25 | | 23 | 0.19 | | 31 | 0.19 | | 82 | 0.16 | | 39 | 0.15 | | 34 | 0.12 |
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Frequency Analysis based on Quarterly Comb
Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 82.00
Sawtooth = 49.88
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 51.38 | 87.00 | 55.00 | 57.70 % | | Low | 51.50 | 92.00 | 76.00 | 24.88 % |
| Recent High | Price | Recent Low | Price | Cycle | | Wednesday, January 06, 2010 | 31.43 | | | 49 | | | Friday, November 27, 2009 | 19.66 | 184 | | Monday, October 26, 2009 | 24.01 | | | 67 | | | Monday, March 09, 2009 | 7.65 | 72 | | Wednesday, July 22, 2009 | 18.99 | | | 136 | | | Thursday, November 20, 2008 | 5.32 | 82 | | Tuesday, January 06, 2009 | 12.94 | | | 74 | | | Monday, July 28, 2008 | 13.35 | 89 |
Fourier Transform after Digital Filter Q | Cycle Length | Fourier Amplitude | | 8 | 0.33 | | 85 | 0.23 | | 14 | 0.23 | | 341 | 0.21 | | 128 | 0.18 | | 293 | 0.16 | | 73 | 0.16 | | 18 | 0.15 | | 205 | 0.15 | | 57 | 0.12 | | 31 | 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, November 20, 2008 | 5.32 | 438 | | Tuesday, September 04, 2007 | 58.10 | | | 412 | | | Wednesday, February 28, 2007 | 36.42 | 151 | | Thursday, January 12, 2006 | 77.22 | | | 545 | | | Friday, July 21, 2006 | 37.51 | 514 | | Wednesday, November 12, 2003 | 42.49 | | | 398 | | | Thursday, July 08, 2004 | 19.61 | 514 | | Wednesday, April 17, 2002 | 11.53 | | | 527 |
Fourier Transform on Raw Closing Prices | Cycle Length | Fourier Amplitude | | 512 | 7.92 | | 683 | 4.80 | | 205 | 2.74 | | 293 | 2.73 | | 256 | 2.61 | | 341 | 2.10 | | 410 | 1.85 | | 85 | 1.63 | | 102 | 1.54 | | 228 | 1.52 | | 11 | 1.38 |
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| Breaking News: In the news, Friday, March 12, 2010: An unfavorable condition has developed with Convergys Corporation, ticker symbol CVG. Also, there are breaking events concerning ConAgra Foods, Inc. (CAG) and Pre-Paid Legal (PPD)
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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 - 0 instances | | | | Sell Signals - 8 instances | | Future30SesAvgClose | 5.00 % minus 3.68 % = 1.32 % | 11.19 % | | Future5SesAvgClose | 2.89 % minus 0.70 % = 2.19 % | 111.47 % | | Future2SesAvgClose | 2.02 % minus 0.35 % = 1.67 % | 212.69 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 13 instances | | | | Future30SesAvgClose | 11.94 % minus 3.68 % = 8.26 % | 69.96 % | | Future5SesAvgClose | 3.50 % minus 0.70 % = 2.80 % | 142.22 % | | Future2SesAvgClose | 1.17 % minus 0.35 % = 0.82 % | 104.47 % | | Sell Signals - 12 instances | | Future30SesAvgClose | 11.44 % minus 3.68 % = 7.76 % | 65.73 % | | Future5SesAvgClose | 0.11 % minus 0.70 % = -0.59 % | -30.12 % | | Future2SesAvgClose | 0.37 % minus 0.35 % = 0.02 % | 2.56 % | | . | | | 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 - 9 instances | | Future30SesAvgClose | 0.75 % minus 3.68 % = -2.93 % | -24.79 % | | Future5SesAvgClose | -6.68 % minus 0.70 % = -7.38 % | -374.85 % | | Future2SesAvgClose | -4.34 % minus 0.35 % = -4.68 % | -594.99 % | | . | | | Projection of Representative Monthly Cycle | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 58 instances | | | | Future30SesAvgClose | 2.86 % minus 3.68 % = -0.82 % | -6.97 % | | Future5SesAvgClose | -0.61 % minus 0.70 % = -1.30 % | -66.22 % | | Future2SesAvgClose | -0.78 % minus 0.35 % = -1.13 % | -143.35 % | | Sell Signals - 59 instances | | Future30SesAvgClose | 1.20 % minus 3.68 % = -2.48 % | -20.99 % | | Future5SesAvgClose | 0.51 % minus 0.70 % = -0.19 % | -9.41 % | | Future2SesAvgClose | 0.41 % minus 0.35 % = 0.06 % | 7.42 % | | . | | | Projection of BiWeekly Modal Cycles | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 136 instances | | | | Future30SesAvgClose | 4.62 % minus 3.68 % = 0.94 % | 7.96 % | | Future5SesAvgClose | 0.70 % minus 0.70 % = 0.00 % | -0.02 % | | Future2SesAvgClose | 0.02 % minus 0.35 % = -0.33 % | -41.83 % | | Sell Signals - 116 instances | | Future30SesAvgClose | 4.45 % minus 3.68 % = 0.77 % | 6.53 % | | Future5SesAvgClose | 0.02 % minus 0.70 % = -0.67 % | -34.22 % | | Future2SesAvgClose | -0.29 % minus 0.35 % = -0.64 % | -80.78 % | | . | | | | |
| The best buy signal for 30 future sessions was 8.26 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing,and the best sell signal for was -2.93 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30. | | For 5 future sessions the best buy signal was 2.80 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing,and the best sell signal was -7.38 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30. | | The best buy signal for 2 future sessions was 0.82 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing,and the best sell signal was -4.68 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30. |
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