Periodic Frequencies for C

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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 14 trading sessions.

Frequency Analysis based on Monthly Comb

Frequency Analysis based on Monthly Comb of CitiGroup

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, 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 CitiGroup:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 27.00
Sawtooth = 50.41
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.5930.0026.0012.98 %
Low16.8332.0017.0012.17 %
Recent HighPriceRecent LowPrice Cycle
Wednesday, October 13, 20104.2522
Thursday, September 23, 20103.8019
Monday, September 13, 20103.9929
Thursday, August 26, 20103.6641
Monday, August 02, 20104.1914
Tuesday, June 29, 20103.7327
Tuesday, July 13, 20104.3015
Thursday, May 20, 20103.6380


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
140.55
120.53
160.47
200.38
220.33
180.31
260.31
280.25
330.22
380.18
560.15



Frequency Analysis based on Quarterly Comb

Frequency Analysis based on Quarterly Comb of CitiGroup

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 68.00
Sawtooth = 49.10
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High50.6090.0068.0024.23 %
Low48.5797.00110.0014.49 %
Recent HighPriceRecent LowPrice Cycle
Thursday, August 26, 20103.6668
Tuesday, July 13, 20104.3058
Thursday, May 20, 20103.6380
Tuesday, April 20, 20104.97160
Tuesday, January 26, 20103.15137
Friday, August 28, 20095.2378
Friday, July 10, 20092.5988
Friday, May 08, 20094.02151


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
140.28
170.21
230.20
1240.19
200.18
530.16
550.16
1000.15
260.15
280.14
340.13



Frequency Analysis based on Yearly Comb

Frequency Analysis based on Yearly Comb of CitiGroup

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 48.41
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Tuesday, April 20, 20104.97160
Thursday, March 05, 20091.02887
Friday, August 28, 20095.23672
Wednesday, August 24, 200537.01211
Wednesday, December 27, 200651.01477
Friday, October 22, 200435.24568
Friday, February 04, 200541.97213
Tuesday, July 23, 200219.60210


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
8194.04
6831.20
121.06
2930.99
4550.91
3410.90
140.86
4100.83
3150.71
5120.70
5850.67




Breaking News:

Monday, November 15, 2010: We have news on PG&E Corporation, ticker symbol PCG. A significant moving average event has happened. Also, there are breaking events concerning Cree, Inc. and Abbott Laboratories.

From the News Archive: (11/12/2010 ) A favorable event happened at PetSmart, Inc. Meanwhile, bad news came from Intel, Chesapeake Energy Corporation, and JP Morgan Chase.



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C




CitiGroup












Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of CitiGroup

C




CitiGroup









Average Sawtooth based on Bi-weekly Combo

C:  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 - 4 instances
Future30SesAvgClose -1.61 % minus 1.65 % = -3.26 %-27.63 %
Future5SesAvgClose -0.56 % minus 0.33 % = -0.89 %-45.01 %
Future2SesAvgClose -0.56 % minus 0.17 % = -0.72 %-91.95 %
Sell Signals - 12 instances
Future30SesAvgClose 3.48 % minus 1.65 % = 1.82 %15.45 %
Future5SesAvgClose 1.37 % minus 0.33 % = 1.04 %52.64 %
Future2SesAvgClose 1.64 % minus 0.17 % = 1.47 %186.29 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle CrossingSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 53 instances
Future30SesAvgClose 1.08 % minus 1.65 % = -0.58 %-4.87 %
Future5SesAvgClose -0.31 % minus 0.33 % = -0.64 %-32.43 %
Future2SesAvgClose -0.25 % minus 0.17 % = -0.42 %-53.29 %
Sell Signals - 50 instances
Future30SesAvgClose 1.87 % minus 1.65 % = 0.22 %1.87 %
Future5SesAvgClose 0.04 % minus 0.33 % = -0.29 %-14.71 %
Future2SesAvgClose -0.31 % minus 0.17 % = -0.48 %-60.70 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 10 instances
Future30SesAvgClose 2.56 % minus 1.65 % = 0.91 %7.72 %
Future5SesAvgClose 1.79 % minus 0.33 % = 1.46 %74.30 %
Future2SesAvgClose 1.78 % minus 0.17 % = 1.61 %204.19 %
Sell Signals - 13 instances
Future30SesAvgClose 2.77 % minus 1.65 % = 1.11 %9.44 %
Future5SesAvgClose 1.08 % minus 0.33 % = 0.75 %37.94 %
Future2SesAvgClose 0.54 % minus 0.17 % = 0.37 %47.44 %
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 161 instances
Future30SesAvgClose 2.90 % minus 1.65 % = 1.25 %10.56 %
Future5SesAvgClose 1.05 % minus 0.33 % = 0.72 %36.55 %
Future2SesAvgClose 0.35 % minus 0.17 % = 0.18 %22.54 %
Sell Signals - 177 instances
Future30SesAvgClose 1.20 % minus 1.65 % = -0.45 %-3.84 %
Future5SesAvgClose 0.25 % minus 0.33 % = -0.08 %-4.17 %
Future2SesAvgClose 0.18 % minus 0.17 % = 0.01 %1.52 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 348 instances
Future30SesAvgClose 2.11 % minus 1.65 % = 0.46 %3.89 %
Future5SesAvgClose 0.50 % minus 0.33 % = 0.17 %8.83 %
Future2SesAvgClose 0.13 % minus 0.17 % = -0.04 %-4.66 %
Sell Signals - 359 instances
Future30SesAvgClose 1.42 % minus 1.65 % = -0.23 %-1.95 %
Future5SesAvgClose 0.01 % minus 0.33 % = -0.32 %-16.35 %
Future2SesAvgClose -0.15 % minus 0.17 % = -0.31 %-39.88 %
.
The best buy signal for 30 future sessions was 1.25 % from the Projection of Representative Monthly Cycle,and the best sell signal for was -0.45 % from the Projection of Representative Monthly Cycle.
For 5 future sessions the best buy signal was 1.46 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.32 % from the Projection of BiWeekly Modal Cycles.
The best buy signal for 2 future sessions was 1.61 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.48 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.



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