Frequency Analysis of MSO

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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 8 trading sessions.

Frequency Analysis based on Monthly Comb

Frequency Analysis based on Monthly Comb of Martha Stewart

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.

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 Martha Stewart:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 23.00
Sawtooth = 54.29
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.5028.0024.0028.18 %
Low16.6331.0023.0033.06 %
Recent HighPriceRecent LowPrice Cycle
Wednesday, February 17, 20105.7626
Friday, January 29, 20104.4319
Friday, January 08, 20105.9722
Thursday, December 31, 20094.9423
Monday, December 07, 20095.2056
Friday, November 27, 20094.5216
Wednesday, November 04, 20094.8084
Thursday, September 17, 20098.4675


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
140.32
170.32
240.30
190.29
340.20
480.18
270.18
310.15
790.13
390.13
4100.12



Frequency Analysis based on Quarterly Comb

Frequency Analysis based on Quarterly Comb of Martha Stewart

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 87.00
Sawtooth = 55.09
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High49.5087.0056.0032.45 %
Low48.6385.00122.0053.66 %
Recent HighPriceRecent LowPrice Cycle
Friday, January 29, 20104.4342
Friday, January 08, 20105.9778
Friday, November 27, 20094.52100
Thursday, September 17, 20098.46110
Wednesday, July 08, 20092.7384
Monday, April 13, 20093.93141
Monday, March 09, 20091.61163
Thursday, September 18, 20089.0687


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
80.33
1140.22
130.21
760.19
200.18
1200.16
1580.15
2280.14
1860.14
1280.14
4100.14



Frequency Analysis based on Yearly Comb

MSO:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 0.00
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Monday, March 09, 20091.61285
Wednesday, December 20, 200623.12322
Friday, January 18, 20085.57376
Monday, September 12, 200533.75139
Friday, July 21, 200615.04510
Wednesday, February 23, 200537.40249
Wednesday, July 14, 20048.54441
Friday, February 27, 200414.53198


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
6833.34
4102.85
2281.72
1711.51
5121.20
1460.98
2050.89
3410.84
1370.80
110.77
2560.71




Breaking News:

In the news, Thursday, March 18, 2010: An unfavorable condition has developed with MicroSoft, ticker symbol MSFT. Also, there are breaking events concerning AOL Time Warner (TWX) and Mylan Inc. (MYL)


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Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of Martha Stewart

Average Sawtooth based on Bi-weekly Combo

Average Sawtooth based on Bi-weeklyly Combo of Martha Stewart



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.

.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 0 instances
Sell Signals - 0 instances
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle CrossingSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 8 instances
Future30SesAvgClose -5.52 % minus 0.02 % = -5.55 %-46.95 %
Future5SesAvgClose -2.36 % minus 0.03 % = -2.38 %-121.15 %
Future2SesAvgClose -1.33 % minus 0.01 % = -1.34 %-170.10 %
Sell Signals - 8 instances
Future30SesAvgClose -5.58 % minus 0.02 % = -5.60 %-47.44 %
Future5SesAvgClose -2.02 % minus 0.03 % = -2.05 %-103.97 %
Future2SesAvgClose -1.89 % minus 0.01 % = -1.90 %-241.55 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 2 instances
Future30SesAvgClose -3.92 % minus 0.02 % = -3.94 %-33.38 %
Future5SesAvgClose -0.93 % minus 0.03 % = -0.96 %-48.71 %
Future2SesAvgClose -2.10 % minus 0.01 % = -2.11 %-267.90 %
Sell Signals - 0 instances
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 34 instances
Future30SesAvgClose 0.55 % minus 0.02 % = 0.53 %4.50 %
Future5SesAvgClose -0.83 % minus 0.03 % = -0.86 %-43.45 %
Future2SesAvgClose -1.13 % minus 0.01 % = -1.14 %-145.05 %
Sell Signals - 31 instances
Future30SesAvgClose -2.50 % minus 0.02 % = -2.52 %-21.32 %
Future5SesAvgClose -0.08 % minus 0.03 % = -0.10 %-5.32 %
Future2SesAvgClose 0.55 % minus 0.01 % = 0.53 %67.68 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 70 instances
Future30SesAvgClose 0.90 % minus 0.02 % = 0.88 %7.46 %
Future5SesAvgClose 0.16 % minus 0.03 % = 0.13 %6.68 %
Future2SesAvgClose 0.45 % minus 0.01 % = 0.44 %55.93 %
Sell Signals - 68 instances
Future30SesAvgClose 0.17 % minus 0.02 % = 0.15 %1.30 %
Future5SesAvgClose 0.62 % minus 0.03 % = 0.59 %30.13 %
Future2SesAvgClose 0.79 % minus 0.01 % = 0.78 %98.55 %
.
The best buy signal for 30 future sessions was 0.88 % from the Projection of BiWeekly Modal Cycles,and the best sell signal for was -5.60 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.
For 5 future sessions the best buy signal was 0.13 % from the Projection of BiWeekly Modal Cycles,and the best sell signal was -2.05 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.
The best buy signal for 2 future sessions was 0.44 % from the Projection of BiWeekly Modal Cycles,and the best sell signal was -1.90 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.



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