Frequency Analysis of GENZ

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From the Update 3/17/2010: The strongest frequency, according to classical frequency analysis, is an oscillation with a length of 16 trading sessions.

Frequency Analysis based on Monthly Comb

GENZ:  Frequency Analysis based on Monthly Comb

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.

In order to determine the actual frequences in a particular case, we must conduct an new form of analysis that is better suited to deal with the oxymoronic condition of variable length cycles.




General Market Conditions

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More than 70 Hi-Rez charts daily for Genzyme Corporation:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 31.00
Sawtooth = 49.32
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.7731.0015.0021.77 %
Low16.9131.0019.0015.32 %
Recent HighPriceRecent LowPrice Cycle
Monday, March 01, 201057.8317
Monday, December 21, 200947.9525
Wednesday, February 03, 201057.0055
Friday, November 13, 200949.2831
Thursday, November 12, 200953.1740
Thursday, October 01, 200955.2238
Thursday, September 17, 200958.2434
Friday, August 07, 200948.1937


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
140.42
190.39
210.34
240.29
290.27
260.24
340.19
410.16
450.14
360.14
760.14



Frequency Analysis based on Quarterly Comb

GENZ:  Frequency Analysis based on Quarterly Comb

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 76.00
Sawtooth = 47.16
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High50.3181.0056.0024.20 %
Low47.6882.0038.0027.94 %
Recent HighPriceRecent LowPrice Cycle
Monday, December 21, 200947.9594
Thursday, September 17, 200958.2474
Friday, August 07, 200948.1975
Wednesday, June 03, 200962.4476
Wednesday, April 22, 200951.3435
Thursday, February 12, 200973.21125
Tuesday, March 03, 200952.4862
Thursday, August 14, 200883.2595


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
160.26
190.20
760.17
1140.16
230.16
260.14
290.14
850.14
410.13
1640.12
1020.12



Frequency Analysis based on Yearly Comb

GENZ:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 41.39
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Thursday, August 14, 200883.25145
Tuesday, August 28, 200758.97323
Thursday, January 17, 200881.13313
Tuesday, May 16, 200655.00500
Wednesday, October 18, 200670.07231
Thursday, May 20, 200441.00470
Wednesday, November 16, 200577.53452
Wednesday, July 10, 200216.88291


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
5124.32
6834.15
8193.54
5852.22
3412.09
1641.91
2561.87
4101.82
191.69
161.52
3721.51




Breaking News:

Friday, March 19, 2010: We have news on L-3 Communications Holdings, Inc., ticker symbol LLL. Signs of an over-bought condition have become noticable. Also, there are breaking events concerning American Tower Corporation and TECO Energy, Inc..

From the News Archive: (3/18/2010 ) Bad news came from Allergan, Inc., Sempra Energy, MicroSoft, and Mylan Inc..



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Average Sawtooth based on Monthly Combo

GENZ:  Average Sawtooth based on Monthly Combo

Average Sawtooth based on Bi-weekly Combo

GENZ:  Average Sawtooth based on Bi-weeklyly Combo



Comparing the length of time from high points to successive lowpoints, against the corresponding time span from the lows to the following periodic highs, gives us the Sawtooth Indicator. 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.




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