Frequency Analysis of HPQ

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From the Update 11/12/2010: 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 Hewlett Packard

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, 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.

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 Hewlett Packard:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 13.00
Sawtooth = 48.24
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.1830.0013.0014.50 %
Low16.4831.0015.0012.82 %
Recent HighPriceRecent LowPrice Cycle
Monday, October 18, 201043.3213
Friday, August 27, 201037.9239
Wednesday, September 29, 201042.5345
Friday, July 02, 201042.7219
Tuesday, July 27, 201047.4727
Monday, June 07, 201045.0784
Thursday, June 17, 201048.1445
Thursday, February 04, 201046.7839


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
100.63
130.62
200.36
240.25
260.24
310.21
470.19
420.18
340.17
400.15
380.14



Frequency Analysis based on Quarterly Comb

Frequency Analysis based on Quarterly Comb of Hewlett Packard

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 91.00
Sawtooth = 54.08
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High50.0374.0053.0021.68 %
Low47.5785.0091.0020.71 %
Recent HighPriceRecent LowPrice Cycle
Friday, August 27, 201037.92142
Wednesday, April 14, 201054.3171
Thursday, February 04, 201046.78230
Wednesday, December 30, 200952.65248
Monday, March 09, 200925.2675
Tuesday, January 06, 200938.7777
Monday, November 17, 200828.8791
Tuesday, September 16, 200847.6489


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
100.43
130.34
180.23
200.22
270.15
220.15
240.15
490.15
1520.14
1710.14
530.14



Frequency Analysis based on Yearly Comb

HPQ:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 42.36
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Wednesday, April 14, 201054.31612
Monday, March 09, 200925.26272
Thursday, February 07, 200839.65877
Tuesday, November 06, 200752.21953
Friday, August 13, 200415.56464
Monday, January 26, 200424.45886
Wednesday, October 09, 200210.23265
Thursday, July 13, 200059.84547


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
8196.29
5123.73
5853.52
4102.08
101.90
6831.83
141.74
2561.29
161.23
3151.17
2281.16




Breaking News:

Friday, November 12, 2010: We have news on Cree, Inc., ticker symbol CREE. Signs of an over-bought condition have become noticable. Also, there are breaking events concerning Intel and PetSmart, Inc.

From the News Archive: (11/11/2010 ) Favorable events happened at Exxon Mobil, Ingersoll-Rand Company Limited, and Concur Technologies, Inc.. Meanwhile, bad news came from International Game Technology.



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HPQ




Hewlett Packard












Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of Hewlett Packard

HPQ




Hewlett Packard









Average Sawtooth based on Bi-weekly Combo

Average Sawtooth based on Bi-weeklyly Combo of Hewlett Packard



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 - 7 instances
Future30SesAvgClose 3.13 % minus 1.93 % = 1.20 %10.16 %
Future5SesAvgClose 1.33 % minus 0.42 % = 0.91 %46.21 %
Future2SesAvgClose 1.72 % minus 0.22 % = 1.50 %190.00 %
Sell Signals - 8 instances
Future30SesAvgClose 0.43 % minus 1.93 % = -1.50 %-12.69 %
Future5SesAvgClose -0.64 % minus 0.42 % = -1.06 %-53.71 %
Future2SesAvgClose -0.17 % minus 0.22 % = -0.39 %-50.15 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle CrossingSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 38 instances
Future30SesAvgClose 2.68 % minus 1.93 % = 0.76 %6.40 %
Future5SesAvgClose 0.62 % minus 0.42 % = 0.20 %10.30 %
Future2SesAvgClose 0.46 % minus 0.22 % = 0.24 %29.95 %
Sell Signals - 36 instances
Future30SesAvgClose -0.88 % minus 1.93 % = -2.81 %-23.78 %
Future5SesAvgClose -0.44 % minus 0.42 % = -0.85 %-43.38 %
Future2SesAvgClose -0.47 % minus 0.22 % = -0.69 %-87.89 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 17 instances
Future30SesAvgClose 2.74 % minus 1.93 % = 0.81 %6.86 %
Future5SesAvgClose 1.20 % minus 0.42 % = 0.79 %39.96 %
Future2SesAvgClose 0.73 % minus 0.22 % = 0.51 %64.95 %
Sell Signals - 10 instances
Future30SesAvgClose 1.29 % minus 1.93 % = -0.64 %-5.44 %
Future5SesAvgClose 0.43 % minus 0.42 % = 0.01 %0.58 %
Future2SesAvgClose 0.64 % minus 0.22 % = 0.41 %52.39 %
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 203 instances
Future30SesAvgClose 1.43 % minus 1.93 % = -0.50 %-4.20 %
Future5SesAvgClose 0.44 % minus 0.42 % = 0.02 %1.15 %
Future2SesAvgClose 0.22 % minus 0.22 % = 0.00 %-0.38 %
Sell Signals - 223 instances
Future30SesAvgClose 1.28 % minus 1.93 % = -0.64 %-5.45 %
Future5SesAvgClose -0.07 % minus 0.42 % = -0.49 %-25.01 %
Future2SesAvgClose -0.16 % minus 0.22 % = -0.38 %-48.48 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 412 instances
Future30SesAvgClose 1.51 % minus 1.93 % = -0.42 %-3.54 %
Future5SesAvgClose 0.14 % minus 0.42 % = -0.27 %-13.87 %
Future2SesAvgClose 0.10 % minus 0.22 % = -0.12 %-15.60 %
Sell Signals - 411 instances
Future30SesAvgClose 1.42 % minus 1.93 % = -0.51 %-4.35 %
Future5SesAvgClose 0.12 % minus 0.42 % = -0.30 %-15.18 %
Future2SesAvgClose 0.10 % minus 0.22 % = -0.12 %-15.61 %
.
The best buy signal for 30 future sessions was 1.20 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25,and the best sell signal for was -2.81 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.
For 5 future sessions the best buy signal was 0.91 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25,and the best sell signal was -1.06 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25.
The best buy signal for 2 future sessions was 1.50 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25,and the best sell signal was -0.69 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.



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