CSCO Periodic Wave Oscillators

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From the Update 3/10/2010: 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 Cisco Systems

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, 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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Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 24.00
Sawtooth = 49.30
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.5330.0022.0018.81 %
Low16.2631.0018.0018.01 %
Recent HighPriceRecent LowPrice Cycle
Friday, January 29, 201022.4728
Thursday, January 14, 201024.9526
Thursday, December 17, 200923.1814
Monday, December 07, 200924.2113
Friday, November 27, 200923.3819
Tuesday, November 17, 200924.0924
Friday, October 30, 200922.8125
Wednesday, October 14, 200924.3817


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
120.62
140.48
180.43
200.35
240.33
270.28
290.20
310.17
340.17
380.16
410.15



Frequency Analysis based on Quarterly Comb

CSCO:  Frequency Analysis based on Quarterly Comb

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 63.00
Sawtooth = 47.33
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High47.5485.0051.0042.14 %
Low47.00104.0047.0026.98 %
Recent HighPriceRecent LowPrice Cycle
Thursday, January 14, 201024.9563
Monday, March 09, 200913.6272
Wednesday, October 14, 200924.38195
Thursday, November 20, 200814.4791
Tuesday, January 06, 200917.7998
Tuesday, July 15, 200821.0463
Friday, August 15, 200824.9150
Tuesday, April 15, 200823.1139


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
100.36
120.32
140.28
180.21
2160.21
1780.20
220.19
260.15
240.15
1710.13
530.13



Frequency Analysis based on Yearly Comb

CSCO:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 54.61
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Monday, March 09, 200913.62651
Tuesday, November 06, 200734.08580
Friday, August 04, 200617.24198
Tuesday, July 19, 200520.17378
Thursday, October 20, 200516.93130
Friday, January 16, 200429.13956
Monday, April 18, 200517.02635
Monday, March 27, 200080.061527


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
8195.40
5853.73
4553.28
4101.99
5121.88
91.77
121.71
3411.70
3721.52
6831.41
2931.19




Breaking News:

Wednesday, March 10, 2010: We have news on Philip Morris, ticker symbol MO. Some signs of an over-sold condition have become evident. Also, there are breaking events concerning PNC Financial Services and NiSource Inc..

From the News Archive: (3/10/2010 ) Bad news came from CenterPoint Energy, Inc., Vulcan Materials Company, Best Buy Co., Inc., and Avon Products, Inc..



Other Companies
Affiliated Computer Services, Inc.
Oracle
Corning
Wisconsin Energy Corporation
Lockheed Martin Corporation
Huntington Bancshares Incorporated
Automatic Data Processing
Harley-Davidson, Inc.
Union Pacific Corporation
LoJack Corp
ACM Income Fund






Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of Cisco Systems

Average Sawtooth based on Bi-weekly Combo

CSCO:  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.

.
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 - 25 instances
Future30SesAvgClose 0.44 % minus 3.03 % = -2.60 %-21.99 %
Future5SesAvgClose 0.74 % minus 0.59 % = 0.14 %7.27 %
Future2SesAvgClose 0.07 % minus 0.30 % = -0.24 %-29.95 %
Sell Signals - 23 instances
Future30SesAvgClose 1.40 % minus 3.03 % = -1.63 %-13.84 %
Future5SesAvgClose -0.26 % minus 0.59 % = -0.86 %-43.64 %
Future2SesAvgClose -0.59 % minus 0.30 % = -0.89 %-112.98 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 3 instances
Future30SesAvgClose 4.64 % minus 3.03 % = 1.61 %13.61 %
Future5SesAvgClose -0.28 % minus 0.59 % = -0.87 %-44.20 %
Future2SesAvgClose 0.13 % minus 0.30 % = -0.18 %-22.47 %
Sell Signals - 5 instances
Future30SesAvgClose 1.00 % minus 3.03 % = -2.03 %-17.23 %
Future5SesAvgClose -2.56 % minus 0.59 % = -3.16 %-160.39 %
Future2SesAvgClose -2.16 % minus 0.30 % = -2.46 %-312.69 %
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 100 instances
Future30SesAvgClose 1.83 % minus 3.03 % = -1.20 %-10.18 %
Future5SesAvgClose -0.19 % minus 0.59 % = -0.78 %-39.86 %
Future2SesAvgClose -0.51 % minus 0.30 % = -0.82 %-103.79 %
Sell Signals - 94 instances
Future30SesAvgClose 2.34 % minus 3.03 % = -0.69 %-5.87 %
Future5SesAvgClose 0.33 % minus 0.59 % = -0.26 %-13.26 %
Future2SesAvgClose 0.12 % minus 0.30 % = -0.18 %-22.72 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 204 instances
Future30SesAvgClose 3.25 % minus 3.03 % = 0.21 %1.82 %
Future5SesAvgClose 0.74 % minus 0.59 % = 0.15 %7.57 %
Future2SesAvgClose 0.40 % minus 0.30 % = 0.10 %12.53 %
Sell Signals - 216 instances
Future30SesAvgClose 1.95 % minus 3.03 % = -1.08 %-9.15 %
Future5SesAvgClose -0.03 % minus 0.59 % = -0.63 %-31.93 %
Future2SesAvgClose -0.26 % minus 0.30 % = -0.56 %-71.07 %
.
The best buy signal for 30 future sessions was 1.61 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal for was -3.03 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25.
For 5 future sessions the best buy signal was 0.15 % from the Projection of BiWeekly Modal Cycles,and the best sell signal was -3.16 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30.
The best buy signal for 2 future sessions was 0.10 % from the Projection of BiWeekly Modal Cycles,and the best sell signal was -2.46 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30.



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