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) = 31.00
Sawtooth = 50.62
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 17.16 | 30.00 | 25.00 | 11.57 % | | Low | 16.24 | 31.00 | 32.00 | 11.33 % |
| Recent High | Price | Recent Low | Price | Cycle | | Wednesday, February 03, 2010 | 54.27 | | | 14 | | | Thursday, January 28, 2010 | 52.61 | 27 | | Wednesday, January 13, 2010 | 55.01 | | | 22 | | | Thursday, December 17, 2009 | 52.76 | 33 | | Thursday, December 10, 2009 | 54.69 | | | 37 | | | Friday, October 30, 2009 | 49.43 | 21 | | Monday, October 19, 2009 | 51.63 | | | 46 | | | Thursday, October 01, 2009 | 48.75 | 58 |
Fourier Transform after Digital Filter M | Cycle Length | Fourier Amplitude | | 14 | 0.52 | | 20 | 0.41 | | 26 | 0.36 | | 33 | 0.25 | | 29 | 0.25 | | 31 | 0.18 | | 38 | 0.17 | | 48 | 0.16 | | 35 | 0.15 | | 43 | 0.12 | | 45 | 0.12 |
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Frequency Analysis based on Quarterly Comb
Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 81.00
Sawtooth = 46.03
| Peak Type | Avg. Cycle | Median Cycle | Cycle Mode | Cycle Amplitude | | High | 49.52 | 81.00 | 135.00 | 18.20 % | | Low | 49.71 | 89.00 | 89.00 | 15.06 % |
| Recent High | Price | Recent Low | Price | Cycle | | Wednesday, January 13, 2010 | 55.01 | | | 105 | | | Thursday, October 01, 2009 | 48.75 | 58 | | Thursday, August 13, 2009 | 51.62 | | | 48 | | | Friday, July 10, 2009 | 47.07 | 108 | | Friday, June 05, 2009 | 50.54 | | | 43 | | | Wednesday, February 04, 2009 | 45.43 | 68 | | Friday, April 03, 2009 | 52.95 | | | 81 | | | Monday, October 27, 2008 | 48.40 | 64 |
Fourier Transform after Digital Filter Q | Cycle Length | Fourier Amplitude | | 12 | 0.33 | | 20 | 0.21 | | 26 | 0.19 | | 23 | 0.16 | | 141 | 0.15 | | 33 | 0.13 | | 117 | 0.13 | | 38 | 0.13 | | 59 | 0.13 | | 64 | 0.12 | | 77 | 0.11 |
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Frequency Analysis based on Yearly Comb
Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 65.72
| 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, February 04, 2009 | 45.43 | 354 | | Thursday, September 11, 2008 | 61.56 | | | 322 | | | Monday, September 10, 2007 | 40.48 | 289 | | Monday, June 04, 2007 | 48.79 | | | 149 | | Thursday, October 26, 2006 | 48.67 | | | 232 | | | Monday, July 17, 2006 | 40.30 | 205 | | Wednesday, November 23, 2005 | 46.90 | | | 259 | | | Wednesday, September 21, 2005 | 39.40 | 284 |
Fourier Transform on Raw Closing Prices | Cycle Length | Fourier Amplitude | | 819 | 3.25 | | 585 | 2.10 | | 410 | 1.89 | | 315 | 1.71 | | 13 | 1.66 | | 683 | 1.63 | | 372 | 1.52 | | 341 | 1.50 | | 512 | 1.29 | | 273 | 1.28 | | 195 | 1.12 |
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| Breaking News: Friday, March 12, 2010: We have news on ConAgra Foods, Inc., ticker symbol CAG. Signs of an over-bought condition have become noticable.
Also, there are breaking events concerning Texas Instruments Incorporated and Convergys Corporation.
From the News Archive: (3/11/2010 ) A favorable event happened at Amgen, Inc.. Meanwhile, bad news came from Coach, Inc., Fluor Corporation (NEW), and Automatic Data Processing.
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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 - 6 instances | | | | Future30SesAvgClose | 1.64 % minus 2.28 % = -0.64 % | -5.39 % | | Future5SesAvgClose | 1.22 % minus 0.45 % = 0.77 % | 39.14 % | | Future2SesAvgClose | -0.22 % minus 0.23 % = -0.45 % | -57.64 % | | Sell Signals - 8 instances | | Future30SesAvgClose | 3.72 % minus 2.28 % = 1.44 % | 12.19 % | | Future5SesAvgClose | -1.38 % minus 0.45 % = -1.84 % | -93.32 % | | Future2SesAvgClose | -1.21 % minus 0.23 % = -1.44 % | -182.40 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 52 instances | | | | Future30SesAvgClose | 3.22 % minus 2.28 % = 0.94 % | 7.95 % | | Future5SesAvgClose | 1.26 % minus 0.45 % = 0.80 % | 40.82 % | | Future2SesAvgClose | 0.92 % minus 0.23 % = 0.69 % | 87.79 % | | Sell Signals - 49 instances | | Future30SesAvgClose | -0.55 % minus 2.28 % = -2.83 % | -23.96 % | | Future5SesAvgClose | -0.76 % minus 0.45 % = -1.21 % | -61.61 % | | Future2SesAvgClose | -0.29 % minus 0.23 % = -0.52 % | -66.00 % | | . | | | Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30 | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 13 instances | | | | Future30SesAvgClose | 4.00 % minus 2.28 % = 1.72 % | 14.54 % | | Future5SesAvgClose | 2.00 % minus 0.45 % = 1.55 % | 78.69 % | | Future2SesAvgClose | 1.32 % minus 0.23 % = 1.09 % | 138.26 % | | Sell Signals - 19 instances | | Future30SesAvgClose | 1.63 % minus 2.28 % = -0.65 % | -5.49 % | | Future5SesAvgClose | -1.02 % minus 0.45 % = -1.48 % | -75.07 % | | Future2SesAvgClose | -0.73 % minus 0.23 % = -0.96 % | -122.35 % | | . | | | Projection of Representative Monthly Cycle | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 213 instances | | | | Future30SesAvgClose | 2.01 % minus 2.28 % = -0.28 % | -2.33 % | | Future5SesAvgClose | 0.61 % minus 0.45 % = 0.16 % | 7.94 % | | Future2SesAvgClose | 0.18 % minus 0.23 % = -0.05 % | -6.73 % | | Sell Signals - 229 instances | | Future30SesAvgClose | 1.92 % minus 2.28 % = -0.36 % | -3.02 % | | Future5SesAvgClose | 0.52 % minus 0.45 % = 0.06 % | 3.28 % | | Future2SesAvgClose | 0.09 % minus 0.23 % = -0.14 % | -17.37 % | | . | | | Projection of BiWeekly Modal Cycles | Signaled Appreciation minus non-signaled Appreciation | Annualized % | | Buy Signals - 469 instances | | | | Future30SesAvgClose | 1.61 % minus 2.28 % = -0.67 % | -5.64 % | | Future5SesAvgClose | 0.27 % minus 0.45 % = -0.18 % | -9.14 % | | Future2SesAvgClose | 0.17 % minus 0.23 % = -0.06 % | -7.86 % | | Sell Signals - 500 instances | | Future30SesAvgClose | 2.02 % minus 2.28 % = -0.27 % | -2.25 % | | Future5SesAvgClose | 0.44 % minus 0.45 % = -0.01 % | -0.61 % | | Future2SesAvgClose | 0.21 % minus 0.23 % = -0.02 % | -2.28 % | | . | | | | |
| The best buy signal for 30 future sessions was 1.72 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal for was -2.83 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing. | | For 5 future sessions the best buy signal was 1.55 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -1.84 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. | | The best buy signal for 2 future sessions was 1.09 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -1.44 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25. |
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