Frequency Analysis of PX

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

Frequency Analysis based on Monthly Comb

PX:  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.

The paradoxical condition of variable length periods forces the adoptation of some new forms of analysis.




General Market Conditions

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More than 70 Hi-Rez charts daily for Praxair, Inc.:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 28.00
Sawtooth = 47.76
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High17.2328.0019.009.89 %
Low16.7628.0018.009.82 %
Recent HighPriceRecent LowPrice Cycle
Monday, October 25, 201093.7748
Thursday, August 26, 201085.1440
Tuesday, August 17, 201088.6840
Wednesday, June 30, 201075.6028
Monday, June 21, 201081.4139
Thursday, May 20, 201073.4659
Monday, April 26, 201087.3147
Thursday, February 25, 201073.7613


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
110.61
170.51
140.42
200.39
250.32
310.22
290.22
380.17
340.16
450.13
590.13



Frequency Analysis based on Quarterly Comb

PX:  Frequency Analysis based on Quarterly Comb

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 38.00
Sawtooth = 44.88
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High48.7180.0038.0023.43 %
Low45.0781.0038.0014.39 %
Recent HighPriceRecent LowPrice Cycle
Thursday, May 20, 201073.4672
Monday, April 26, 201087.3170
Friday, February 05, 201072.78148
Wednesday, January 13, 201081.4438
Tuesday, November 17, 200983.07138
Tuesday, July 07, 200965.5588
Monday, May 04, 200974.9058
Monday, March 02, 200951.8467


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
110.38
170.23
200.21
250.20
530.15
590.14
380.14
2050.13
460.12
640.12
310.12



Frequency Analysis based on Yearly Comb

Frequency Analysis based on Yearly Comb of Praxair, Inc.

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 49.28
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Friday, February 05, 201072.78303
Monday, June 23, 200894.601583
Thursday, November 20, 200845.641596
Monday, March 11, 200226.10199
Tuesday, July 23, 200219.73208
Thursday, May 17, 200122.97335
Friday, September 21, 200115.97226
Tuesday, January 11, 200022.62170


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
6836.16
5125.11
5855.02
8194.42
4553.20
2732.70
2562.64
142.49
2932.24
1951.98
2411.88




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PX




Praxair, Inc.












Average Sawtooth based on Monthly Combo

PX:  Average Sawtooth based on Monthly Combo

PX




Praxair, Inc.









Average Sawtooth based on Bi-weekly Combo

Average Sawtooth based on Bi-weeklyly Combo of Praxair, Inc.



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.




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