Frequency Analysis of GD

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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

GD:  Frequency Analysis based on Monthly Comb

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.

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 General Dynamics:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 18.00
Sawtooth = 46.07
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.6230.0015.0011.09 %
Low16.7831.0018.009.93 %
Recent HighPriceRecent LowPrice Cycle
Monday, February 08, 201066.3525
Thursday, January 14, 201071.1021
Thursday, December 31, 200967.8022
Monday, December 14, 200970.2819
Monday, November 30, 200965.5418
Monday, November 16, 200967.8420
Tuesday, November 03, 200962.2155
Monday, October 19, 200968.3393


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
100.65
150.44
210.42
170.40
290.25
260.24
330.22
370.20
410.12
350.11
570.11



Frequency Analysis based on Quarterly Comb

GD:  Frequency Analysis based on Quarterly Comb

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 101.00
Sawtooth = 49.96
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High49.47101.00101.0014.00 %
Low50.1198.0041.0016.96 %
Recent HighPriceRecent LowPrice Cycle
Monday, October 19, 200968.3393
Thursday, July 09, 200950.9785
Monday, June 08, 200959.39105
Monday, March 09, 200935.3766
Tuesday, January 06, 200959.26101
Monday, December 01, 200846.9899
Tuesday, August 12, 200890.7359
Friday, July 11, 200878.03119


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
100.39
140.26
210.22
170.21
870.17
1020.15
1710.14
290.13
910.12
670.12
1520.12



Frequency Analysis based on Yearly Comb

GD:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 38.59
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Monday, March 09, 200935.37397
Tuesday, August 12, 200890.731546
Thursday, August 09, 200770.391111
Friday, June 21, 200248.52777
Wednesday, March 12, 200323.22288
Monday, May 10, 199930.921409
Wednesday, January 16, 200232.92462
Friday, October 08, 19937.591074


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
3724.27
4553.82
6833.59
5123.07
3152.48
122.29
3412.28
4102.26
2932.00
141.81
8191.69




Breaking News:

Friday, March 19, 2010: We have news on AutoNation, Inc., ticker symbol AN. A significant moving average event has happened. Also, there are breaking events concerning Abbott Laboratories and Electronic Data Systems.

From the News Archive: (3/19/2010 ) A favorable event happened at Noble Corporation. Meanwhile, bad news came from L-3 Communications Holdings, Inc., AT and T, and American Tower Corporation.



Other Companies
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Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of General Dynamics

Average Sawtooth based on Bi-weekly Combo

GD:  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.

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 - 5 instances
Future30SesAvgClose 3.14 % minus 2.74 % = 0.41 %3.45 %
Future5SesAvgClose -0.30 % minus 0.57 % = -0.87 %-44.12 %
Future2SesAvgClose -1.22 % minus 0.30 % = -1.52 %-192.47 %
Sell Signals - 3 instances
Future30SesAvgClose 2.73 % minus 2.74 % = -0.01 %-0.08 %
Future5SesAvgClose 0.39 % minus 0.57 % = -0.18 %-9.21 %
Future2SesAvgClose 0.51 % minus 0.30 % = 0.21 %26.81 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle CrossingSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 58 instances
Future30SesAvgClose 2.62 % minus 2.74 % = -0.12 %-1.02 %
Future5SesAvgClose 0.53 % minus 0.57 % = -0.04 %-2.27 %
Future2SesAvgClose 0.32 % minus 0.30 % = 0.02 %2.82 %
Sell Signals - 58 instances
Future30SesAvgClose 0.49 % minus 2.74 % = -2.25 %-19.07 %
Future5SesAvgClose -0.18 % minus 0.57 % = -0.76 %-38.39 %
Future2SesAvgClose -0.03 % minus 0.30 % = -0.33 %-41.33 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 11 instances
Future30SesAvgClose 1.73 % minus 2.74 % = -1.00 %-8.49 %
Future5SesAvgClose 1.20 % minus 0.57 % = 0.63 %32.07 %
Future2SesAvgClose 0.57 % minus 0.30 % = 0.27 %34.79 %
Sell Signals - 9 instances
Future30SesAvgClose 4.55 % minus 2.74 % = 1.82 %15.39 %
Future5SesAvgClose 1.52 % minus 0.57 % = 0.95 %48.29 %
Future2SesAvgClose 1.02 % minus 0.30 % = 0.72 %90.84 %
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 145 instances
Future30SesAvgClose 1.79 % minus 2.74 % = -0.94 %-7.98 %
Future5SesAvgClose 0.12 % minus 0.57 % = -0.45 %-22.75 %
Future2SesAvgClose 0.21 % minus 0.30 % = -0.09 %-11.91 %
Sell Signals - 175 instances
Future30SesAvgClose 2.12 % minus 2.74 % = -0.62 %-5.26 %
Future5SesAvgClose 0.51 % minus 0.57 % = -0.06 %-2.99 %
Future2SesAvgClose 0.31 % minus 0.30 % = 0.01 %0.99 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 338 instances
Future30SesAvgClose 2.56 % minus 2.74 % = -0.17 %-1.47 %
Future5SesAvgClose 0.51 % minus 0.57 % = -0.06 %-3.05 %
Future2SesAvgClose 0.32 % minus 0.30 % = 0.02 %3.06 %
Sell Signals - 367 instances
Future30SesAvgClose 2.91 % minus 2.74 % = 0.18 %1.50 %
Future5SesAvgClose 0.69 % minus 0.57 % = 0.12 %5.96 %
Future2SesAvgClose 0.45 % minus 0.30 % = 0.15 %18.95 %
.
The best buy signal for 30 future sessions was 0.41 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25,and the best sell signal for was -2.25 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.
For 5 future sessions the best buy signal was 0.63 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.76 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.
The best buy signal for 2 future sessions was 0.27 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.33 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.



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