Frequency Analysis of UST

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From the Update 7/22/2009: The strongest frequency, according to classical frequency analysis, is an oscillation with a length of 14 trading sessions.

Frequency Analysis based on Monthly Comb

UST:  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, attempts to exploit the market cycles are foiled by the deviation from strictly periodic behavior required by ordinary analysis.

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 UST Inc.:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 32.00
Sawtooth = 47.66
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High17.3432.0023.0011.67 %
Low16.3432.0019.0010.66 %
Recent HighPriceRecent LowPrice Cycle
Friday, January 02, 200969.4633
Thursday, November 20, 200867.4329
Thursday, November 13, 200868.5140
Friday, October 10, 200859.4553
Thursday, September 18, 200867.7059
Monday, July 28, 200849.1225
Wednesday, June 25, 200854.8143
Friday, June 20, 200852.4134


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
140.45
180.37
200.34
240.25
280.23
260.23
310.18
630.17
360.16
330.16
390.15



Frequency Analysis based on Quarterly Comb

Frequency Analysis based on Quarterly Comb of UST Inc.

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 37.00
Sawtooth = 43.66
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High49.4781.0037.0028.72 %
Low49.6090.0051.0014.37 %
Recent HighPriceRecent LowPrice Cycle
Friday, January 02, 200969.4673
Monday, July 28, 200849.1259
Thursday, September 18, 200867.7059
Friday, May 02, 200849.9664
Wednesday, June 25, 200854.8199
Thursday, January 31, 200849.89112
Monday, February 04, 200854.6937
Tuesday, August 21, 200745.0451


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
140.27
200.19
260.16
1200.16
1520.15
630.14
1780.14
910.14
290.13
4550.12
530.12



Frequency Analysis based on Yearly Comb

UST:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 41.74
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Friday, January 02, 200969.46268
Monday, July 28, 200849.12235
Monday, December 10, 200756.52204
Tuesday, August 21, 200745.04429
Tuesday, February 20, 200755.71493
Monday, December 05, 200532.49798
Friday, March 04, 200547.03436
Friday, October 04, 200218.61550


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
8194.87
5853.95
5123.69
4553.61
3412.49
6832.20
4101.93
2561.84
2931.76
3151.58
1781.27




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Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of UST Inc.

Average Sawtooth based on Bi-weekly Combo

UST:  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.

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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