Frequency Analysis of LOJN

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From the Update 11/5/2010: The strongest frequency, according to classical frequency analysis, is an oscillation with a length of 18 trading sessions.

Frequency Analysis based on Monthly Comb

Frequency Analysis based on Monthly Comb of LoJack Corp

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.

In order to determine the actual frequences in a particular case, we must conduct an new form of analysis that is better suited to deal with the oxymoronic condition of variable length cycles.




General Market Conditions

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More than 70 Hi-Rez charts daily for LoJack Corp:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 25.00
Sawtooth = 50.95
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.8826.0023.0019.26 %
Low17.0329.0027.0017.23 %
Recent HighPriceRecent LowPrice Cycle
Tuesday, August 31, 20103.3225
Monday, August 09, 20103.7830
Tuesday, July 27, 20103.4514
Friday, June 25, 20103.9530
Wednesday, July 07, 20103.4042
Thursday, May 13, 20104.5813
Thursday, May 06, 20103.9925
Monday, April 26, 20104.8038


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
180.51
160.46
200.41
230.29
340.21
290.21
390.19
530.14
470.13
430.12
840.10



Frequency Analysis based on Quarterly Comb

Frequency Analysis based on Quarterly Comb of LoJack Corp

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 70.00
Sawtooth = 47.87
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High47.5586.0070.0028.20 %
Low49.4587.0086.0041.57 %
Recent HighPriceRecent LowPrice Cycle
Tuesday, August 31, 20103.3239
Monday, April 26, 20104.8038
Wednesday, July 07, 20103.40154
Tuesday, March 02, 20104.60131
Monday, November 23, 20093.76121
Friday, August 21, 20095.6088
Wednesday, June 03, 20093.2061
Friday, April 17, 20095.4070


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
180.27
200.23
160.22
250.18
230.18
1000.17
1280.17
310.16
290.15
470.15
930.14



Frequency Analysis based on Yearly Comb

LOJN:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 25.48
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Friday, August 21, 20095.60526
Friday, March 06, 20092.67569
Monday, July 23, 200724.01409
Wednesday, November 29, 200614.971115
Friday, December 02, 200528.84502
Thursday, June 27, 20023.37274
Friday, December 05, 20039.00404
Friday, May 18, 20014.90198


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
5121.27
5851.00
4100.75
4550.52
8190.46
2560.46
140.46
2280.43
6830.42
160.41
3410.39




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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LOJN




LoJack Corp












Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of LoJack Corp

LOJN




LoJack Corp









Average Sawtooth based on Bi-weekly Combo

LOJN:  Average Sawtooth based on Bi-weeklyly Combo



Comparing the length of time from high points to successive lowpoints, against the corresponding time span from the lows to the following periodic highs, gives us the Sawtooth Indicator. 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 - 24 instances
Future30SesAvgClose 0.08 % minus 0.87 % = -0.79 %-6.68 %
Future5SesAvgClose 0.28 % minus 0.18 % = 0.10 %4.98 %
Future2SesAvgClose 0.52 % minus 0.10 % = 0.42 %53.78 %
Sell Signals - 25 instances
Future30SesAvgClose -2.75 % minus 0.87 % = -3.62 %-30.66 %
Future5SesAvgClose -0.68 % minus 0.18 % = -0.87 %-44.07 %
Future2SesAvgClose 0.08 % minus 0.10 % = -0.01 %-1.71 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 4 instances
Future30SesAvgClose 3.03 % minus 0.87 % = 2.16 %18.30 %
Future5SesAvgClose -0.74 % minus 0.18 % = -0.92 %-46.77 %
Future2SesAvgClose -1.12 % minus 0.10 % = -1.21 %-154.08 %
Sell Signals - 0 instances
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 88 instances
Future30SesAvgClose 2.12 % minus 0.87 % = 1.25 %10.56 %
Future5SesAvgClose 0.96 % minus 0.18 % = 0.78 %39.66 %
Future2SesAvgClose 0.47 % minus 0.10 % = 0.37 %46.69 %
Sell Signals - 86 instances
Future30SesAvgClose 0.51 % minus 0.87 % = -0.36 %-3.03 %
Future5SesAvgClose 0.16 % minus 0.18 % = -0.02 %-0.93 %
Future2SesAvgClose 0.10 % minus 0.10 % = 0.00 %0.12 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 173 instances
Future30SesAvgClose 0.24 % minus 0.87 % = -0.63 %-5.33 %
Future5SesAvgClose 0.15 % minus 0.18 % = -0.03 %-1.58 %
Future2SesAvgClose 0.15 % minus 0.10 % = 0.05 %6.24 %
Sell Signals - 176 instances
Future30SesAvgClose 1.14 % minus 0.87 % = 0.27 %2.31 %
Future5SesAvgClose 0.10 % minus 0.18 % = -0.08 %-4.01 %
Future2SesAvgClose 0.02 % minus 0.10 % = -0.08 %-10.03 %
.
The best buy signal for 30 future sessions was 2.16 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal for was -3.62 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.
For 5 future sessions the best buy signal was 0.78 % from the Projection of Representative Monthly Cycle,and the best sell signal was -0.87 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing.
The best buy signal for 2 future sessions was 0.42 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle Crossing,and the best sell signal was -0.08 % from the Projection of BiWeekly Modal Cycles.



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