Periodic Frequencies for TYC

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From the Update 3/18/2010: The strongest frequency, according to classical frequency analysis, is an oscillation with a length of 11 trading sessions.

Frequency Analysis based on Monthly Comb

TYC:  Frequency Analysis based on Monthly Comb

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, 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.




General Market Conditions

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More than 70 Hi-Rez charts daily for Tyco:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 16.00
Sawtooth = 49.59
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High17.0229.0016.0013.89 %
Low16.9432.0027.0014.66 %
Recent HighPriceRecent LowPrice Cycle
Monday, February 08, 201033.9541
Tuesday, January 19, 201037.9824
Friday, December 11, 200936.3116
Tuesday, December 08, 200934.8825
Wednesday, November 18, 200936.8822
Monday, November 02, 200933.3521
Monday, October 19, 200935.5019
Friday, October 02, 200932.9462


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
120.59
140.49
190.35
230.34
260.33
300.23
380.18
330.17
590.16
400.14
420.13



Frequency Analysis based on Quarterly Comb

Frequency Analysis based on Quarterly Comb of Tyco

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 90.00
Sawtooth = 45.50
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High46.5590.0057.0025.23 %
Low49.0077.0044.0027.05 %
Recent HighPriceRecent LowPrice Cycle
Tuesday, January 19, 201037.9840
Tuesday, July 07, 200925.0983
Wednesday, November 18, 200936.88120
Monday, March 09, 200916.9672
Monday, June 01, 200928.34100
Thursday, November 20, 200815.0991
Tuesday, January 06, 200923.91102
Tuesday, July 15, 200836.96121


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
110.35
150.26
200.19
220.18
260.18
240.18
850.16
1050.14
1240.13
300.13
650.12



Frequency Analysis based on Yearly Comb

TYC:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 40.54
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Thursday, November 20, 200815.09212
Friday, April 18, 200845.29212
Tuesday, January 22, 200832.10494
Friday, June 15, 2007110.06360
Thursday, February 02, 200677.91728
Monday, January 09, 200697.52253
Thursday, January 06, 2005112.75777
Friday, March 14, 200335.41160


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
68311.75
8199.79
2735.30
3155.17
104.84
3414.68
4554.61
5124.22
2933.88
143.75
5853.68




Breaking News:

Thursday, March 18, 2010: We have news on MicroSoft, ticker symbol MSFT. Signs of an over-bought condition have become noticable. Also, there are breaking events concerning Mylan Inc. and LoJack Corp.

From the News Archive: (3/17/2010 ) Bad news came from Masco Corporation, Patterson Companies, Inc., Walmart, and Sempra Energy.



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Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of Tyco

Average Sawtooth based on Bi-weekly Combo

TYC:  Average Sawtooth based on Bi-weeklyly 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.

Bullish or bearish moods may be reflected in the steepness of the buying and selling slopes, particularly as they change through time. 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 25Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 2 instances
Future30SesAvgClose -0.44 % minus 1.53 % = -1.98 %-16.73 %
Future5SesAvgClose 1.32 % minus 0.31 % = 1.01 %51.15 %
Future2SesAvgClose 0.16 % minus 0.16 % = 0.01 %0.66 %
Sell Signals - 0 instances
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle CrossingSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 32 instances
Future30SesAvgClose 0.77 % minus 1.53 % = -0.76 %-6.45 %
Future5SesAvgClose -0.24 % minus 0.31 % = -0.56 %-28.31 %
Future2SesAvgClose 0.16 % minus 0.16 % = 0.01 %0.69 %
Sell Signals - 31 instances
Future30SesAvgClose 2.37 % minus 1.53 % = 0.84 %7.10 %
Future5SesAvgClose 0.66 % minus 0.31 % = 0.35 %17.79 %
Future2SesAvgClose 0.78 % minus 0.16 % = 0.62 %78.82 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 7 instances
Future30SesAvgClose 2.00 % minus 1.53 % = 0.47 %4.00 %
Future5SesAvgClose -1.46 % minus 0.31 % = -1.77 %-90.04 %
Future2SesAvgClose -1.15 % minus 0.16 % = -1.31 %-166.77 %
Sell Signals - 1 instances
Future30SesAvgClose 3.05 % minus 1.53 % = 1.52 %12.83 %
Future5SesAvgClose 3.45 % minus 0.31 % = 3.13 %159.11 %
Future2SesAvgClose 2.08 % minus 0.16 % = 1.92 %244.23 %
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 116 instances
Future30SesAvgClose 1.38 % minus 1.53 % = -0.15 %-1.25 %
Future5SesAvgClose 0.52 % minus 0.31 % = 0.21 %10.58 %
Future2SesAvgClose 0.34 % minus 0.16 % = 0.18 %23.42 %
Sell Signals - 128 instances
Future30SesAvgClose 1.75 % minus 1.53 % = 0.22 %1.88 %
Future5SesAvgClose 0.23 % minus 0.31 % = -0.08 %-4.15 %
Future2SesAvgClose 0.11 % minus 0.16 % = -0.05 %-5.72 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 243 instances
Future30SesAvgClose 2.02 % minus 1.53 % = 0.49 %4.16 %
Future5SesAvgClose 0.59 % minus 0.31 % = 0.27 %13.79 %
Future2SesAvgClose 0.33 % minus 0.16 % = 0.17 %21.22 %
Sell Signals - 252 instances
Future30SesAvgClose 1.70 % minus 1.53 % = 0.17 %1.43 %
Future5SesAvgClose 0.51 % minus 0.31 % = 0.20 %9.99 %
Future2SesAvgClose 0.38 % minus 0.16 % = 0.22 %27.98 %
.
The best buy signal for 30 future sessions was 0.49 % from the Projection of BiWeekly Modal Cycles,and the best sell signal for was -1.53 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25.
For 5 future sessions the best buy signal was 1.01 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25,and the best sell signal was -0.16 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25.
The best buy signal for 2 future sessions was 0.18 % from the Projection of Representative Monthly Cycle,and the best sell signal was -0.05 % from the Projection of Representative Monthly Cycle.



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