Periodic Frequencies for MO

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From the Update 3/17/2010: The strongest frequency, according to classical frequency analysis, is an oscillation with a length of 10 trading sessions.

Frequency Analysis based on Monthly Comb

MO:  Frequency Analysis based on Monthly Comb

Short term fluctuations that seem to repeat with a regular frequency are often (even generally) seen in stock price charts. 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 Philip Morris:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 33.00
Sawtooth = 46.06
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.7433.0015.0015.02 %
Low16.7532.0013.0010.63 %
Recent HighPriceRecent LowPrice Cycle
Monday, February 08, 201019.0447
Friday, January 15, 201020.0841
Monday, November 30, 200918.1940
Monday, November 16, 200918.7019
Tuesday, October 20, 200918.0429
Friday, October 02, 200916.8970
Wednesday, September 09, 200917.6464
Wednesday, June 24, 200915.3823


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
140.55
120.55
180.41
250.35
200.34
290.31
270.21
410.18
590.16
530.16
320.16



Frequency Analysis based on Quarterly Comb

Frequency Analysis based on Quarterly Comb of Philip Morris

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 44.00
Sawtooth = 48.83
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High46.4093.0058.0025.50 %
Low49.33101.0044.0017.19 %
Recent HighPriceRecent LowPrice Cycle
Friday, January 15, 201020.08172
Wednesday, June 24, 200915.3879
Tuesday, May 12, 200916.1933
Tuesday, March 03, 200913.3568
Wednesday, March 25, 200916.0845
Thursday, November 20, 200812.9299
Tuesday, January 20, 200915.67110
Wednesday, July 02, 200817.5344


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
100.32
140.31
1460.24
180.22
240.19
840.18
470.16
2160.15
290.15
1780.13
530.13



Frequency Analysis based on Yearly Comb

MO:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 59.85
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Thursday, November 20, 200812.921133
Wednesday, January 09, 200820.99517
Friday, December 16, 200514.00448
Monday, May 24, 20047.56289
Wednesday, March 10, 20049.71445
Tuesday, April 01, 20034.47784
Tuesday, June 04, 20028.65268
Monday, February 14, 20002.52440


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
6831.01
5120.99
3720.90
4550.88
3150.56
120.56
8190.55
5850.55
3410.54
140.51
160.42




Breaking News:

Thursday, March 18, 2010: We have news on MicroSoft, ticker symbol MSFT. Signs of an over-bought condition have become noticable. Also, there are breaking events concerning Mylan Inc. and Goldman Sachs Group, Inc..

From the News Archive: (3/17/2010 ) Favorable events happened at LoJack Corp and Martha Stewart. Meanwhile, bad news came from Patterson Companies, Inc. and LSI Corporation.



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Average Sawtooth based on Monthly Combo

MO:  Average Sawtooth based on Monthly Combo

Average Sawtooth based on Bi-weekly Combo

Average Sawtooth based on Bi-weeklyly Combo of Philip Morris



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.

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 - 4 instances
Future30SesAvgClose -1.31 % minus 2.10 % = -3.41 %-28.86 %
Future5SesAvgClose -0.27 % minus 0.42 % = -0.69 %-35.08 %
Future2SesAvgClose -0.95 % minus 0.22 % = -1.17 %-149.08 %
Sell Signals - 7 instances
Future30SesAvgClose -0.53 % minus 2.10 % = -2.63 %-22.30 %
Future5SesAvgClose 0.05 % minus 0.42 % = -0.37 %-18.84 %
Future2SesAvgClose -0.12 % minus 0.22 % = -0.34 %-43.60 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle CrossingSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 69 instances
Future30SesAvgClose 1.76 % minus 2.10 % = -0.34 %-2.91 %
Future5SesAvgClose 0.39 % minus 0.42 % = -0.03 %-1.57 %
Future2SesAvgClose 0.37 % minus 0.22 % = 0.15 %19.46 %
Sell Signals - 68 instances
Future30SesAvgClose 2.57 % minus 2.10 % = 0.46 %3.93 %
Future5SesAvgClose 0.80 % minus 0.42 % = 0.37 %18.95 %
Future2SesAvgClose 0.46 % minus 0.22 % = 0.24 %30.22 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 9 instances
Future30SesAvgClose 2.66 % minus 2.10 % = 0.56 %4.73 %
Future5SesAvgClose 0.81 % minus 0.42 % = 0.38 %19.55 %
Future2SesAvgClose 1.13 % minus 0.22 % = 0.91 %115.96 %
Sell Signals - 13 instances
Future30SesAvgClose 0.92 % minus 2.10 % = -1.19 %-10.05 %
Future5SesAvgClose 0.79 % minus 0.42 % = 0.37 %18.88 %
Future2SesAvgClose 0.36 % minus 0.22 % = 0.14 %17.35 %
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 209 instances
Future30SesAvgClose 0.94 % minus 2.10 % = -1.16 %-9.84 %
Future5SesAvgClose 0.22 % minus 0.42 % = -0.21 %-10.53 %
Future2SesAvgClose 0.19 % minus 0.22 % = -0.03 %-3.96 %
Sell Signals - 233 instances
Future30SesAvgClose 1.96 % minus 2.10 % = -0.15 %-1.24 %
Future5SesAvgClose 0.17 % minus 0.42 % = -0.25 %-12.70 %
Future2SesAvgClose -0.05 % minus 0.22 % = -0.27 %-33.87 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 475 instances
Future30SesAvgClose 1.42 % minus 2.10 % = -0.68 %-5.78 %
Future5SesAvgClose 0.07 % minus 0.42 % = -0.35 %-17.84 %
Future2SesAvgClose -0.05 % minus 0.22 % = -0.27 %-34.71 %
Sell Signals - 488 instances
Future30SesAvgClose 1.66 % minus 2.10 % = -0.45 %-3.77 %
Future5SesAvgClose 0.40 % minus 0.42 % = -0.02 %-1.16 %
Future2SesAvgClose 0.24 % minus 0.22 % = 0.01 %1.90 %
.
The best buy signal for 30 future sessions was 0.56 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal for was -2.63 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25.
For 5 future sessions the best buy signal was 0.38 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.37 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25.
The best buy signal for 2 future sessions was 0.91 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.34 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25.



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