Periodic Frequencies for MSFT

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From the Update 3/12/2010: The strongest frequency, according to classical frequency analysis, is an oscillation with a length of 10 trading sessions.

Frequency Analysis based on Monthly Comb

Frequency Analysis based on Monthly Comb of MicroSoft

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, 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 MicroSoft:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 17.00
Sawtooth = 52.03
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High17.1733.0017.0014.75 %
Low16.4133.0017.0013.55 %
Recent HighPriceRecent LowPrice Cycle
Monday, February 08, 201027.5986
Tuesday, January 19, 201030.9613
Tuesday, December 29, 200931.2427
Monday, October 05, 200924.4260
Wednesday, November 18, 200929.9739
Friday, July 10, 200922.0657
Thursday, September 24, 200925.7144
Monday, April 20, 200918.2229


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
100.66
120.57
200.39
180.37
270.25
310.22
240.21
370.19
390.18
330.16
490.16



Frequency Analysis based on Quarterly Comb

MSFT:  Frequency Analysis based on Quarterly Comb

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 92.00
Sawtooth = 52.03
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High47.8774.0060.0022.60 %
Low50.4088.0061.0022.89 %
Recent HighPriceRecent LowPrice Cycle
Tuesday, December 29, 200931.24110
Monday, March 09, 200914.8372
Thursday, July 23, 200925.19314
Thursday, November 20, 200817.0592
Monday, July 14, 200824.2092
Thursday, April 24, 200830.4882
Monday, March 03, 200825.87136
Wednesday, December 26, 200734.9637


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
100.38
120.36
180.19
200.18
490.16
1240.15
1370.15
1050.14
250.13
980.13
590.13



Frequency Analysis based on Yearly Comb

Frequency Analysis based on Yearly Comb of MicroSoft

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 46.67
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Monday, March 09, 200914.83688
Thursday, November 01, 200735.27489
Tuesday, June 13, 200620.12305
Monday, November 21, 200526.15257
Tuesday, March 29, 200522.01255
Monday, November 15, 200425.13291
Tuesday, March 23, 200419.82418
Friday, September 19, 200324.45205


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
5122.56
6831.78
8191.76
4101.64
3411.32
121.18
5851.09
2411.02
1951.00
3150.96
160.83




Breaking News:

Friday, March 12, 2010: We have news on ConAgra Foods, Inc., ticker symbol CAG. Signs of an over-bought condition have become noticable. Also, there are breaking events concerning Texas Instruments Incorporated and Convergys Corporation.

From the News Archive: (3/11/2010 ) A favorable event happened at Amgen, Inc.. Meanwhile, bad news came from Coach, Inc., Fluor Corporation (NEW), and Automatic Data Processing.



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Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of MicroSoft

Average Sawtooth based on Bi-weekly Combo

MSFT:  Average Sawtooth based on Bi-weeklyly Combo



The Sawtooth statistic measures the time from each periodic high to the next periodic low, in comparison to the time from that low to the next high point . 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 - 1 instances
Future30SesAvgClose -1.04 % minus 2.34 % = -3.38 %-28.62 %
Future5SesAvgClose -1.50 % minus 0.46 % = -1.95 %-99.20 %
Future2SesAvgClose -0.79 % minus 0.23 % = -1.02 %-129.78 %
Sell Signals - 0 instances
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle CrossingSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 29 instances
Future30SesAvgClose 3.28 % minus 2.34 % = 0.93 %7.90 %
Future5SesAvgClose 1.16 % minus 0.46 % = 0.70 %35.63 %
Future2SesAvgClose 0.56 % minus 0.23 % = 0.33 %41.28 %
Sell Signals - 31 instances
Future30SesAvgClose 0.97 % minus 2.34 % = -1.38 %-11.65 %
Future5SesAvgClose -0.06 % minus 0.46 % = -0.52 %-26.28 %
Future2SesAvgClose -0.50 % minus 0.23 % = -0.74 %-93.43 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 9 instances
Future30SesAvgClose 3.33 % minus 2.34 % = 0.98 %8.32 %
Future5SesAvgClose 0.44 % minus 0.46 % = -0.02 %-0.87 %
Future2SesAvgClose 0.57 % minus 0.23 % = 0.33 %42.22 %
Sell Signals - 4 instances
Future30SesAvgClose 1.95 % minus 2.34 % = -0.39 %-3.31 %
Future5SesAvgClose -0.15 % minus 0.46 % = -0.61 %-30.95 %
Future2SesAvgClose -0.75 % minus 0.23 % = -0.99 %-125.27 %
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 120 instances
Future30SesAvgClose 1.55 % minus 2.34 % = -0.79 %-6.73 %
Future5SesAvgClose -0.18 % minus 0.46 % = -0.64 %-32.35 %
Future2SesAvgClose -0.25 % minus 0.23 % = -0.48 %-60.96 %
Sell Signals - 124 instances
Future30SesAvgClose 2.81 % minus 2.34 % = 0.46 %3.93 %
Future5SesAvgClose 0.53 % minus 0.46 % = 0.08 %3.97 %
Future2SesAvgClose 0.34 % minus 0.23 % = 0.11 %13.41 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 273 instances
Future30SesAvgClose 3.00 % minus 2.34 % = 0.66 %5.56 %
Future5SesAvgClose 0.62 % minus 0.46 % = 0.17 %8.49 %
Future2SesAvgClose 0.25 % minus 0.23 % = 0.01 %1.40 %
Sell Signals - 279 instances
Future30SesAvgClose 1.93 % minus 2.34 % = -0.41 %-3.50 %
Future5SesAvgClose 0.43 % minus 0.46 % = -0.02 %-1.26 %
Future2SesAvgClose 0.21 % minus 0.23 % = -0.03 %-3.34 %
.
The best buy signal for 30 future sessions was 0.98 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal for was -2.34 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25.
For 5 future sessions the best buy signal was 0.70 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing,and the best sell signal was -0.61 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30.
The best buy signal for 2 future sessions was 0.33 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.99 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30.



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