Time Giant Momentum Indicator

Other Cycle Science -- empirical evidence
suggests that a moving average can lead.

Executive Summary

Price turning-point prediction accuracy shows average differences in scores to be large enough to be statistically significant.

Table 1. Average Accuracy Scores

Treatment of broad indexes by the Time Giant price momentum indicator results in a price prediction accuracy score of +1.88 meaning Time Giant leads by +1.88 time periods, on average.  Treatment of broad indexes by the MACD indicator results in an accuracy score of -2.00 meaning the MACD lags by -2.00 time periods, on average.  Lead is good.  Lag is bad.  The point estimate of the size of the overall difference equals +3.82 units.  That is, [(+1.43) minus (-2.39)] equals (+3.82) units of difference. 

Broad indexes seem to be easier to forecast by both indicators.

The "t - test" quantity of -4.90 for broad indexes suggests that the difference in the accuracy scores occurs because the two indicators really do differ in terms of predictive performance.  The "t - test" quantities have a negative sign because of the subtraction of the two sample means, but the negative sign does not invalidate that the difference is statistically significant in this two-tailed test. 

Interpret the rows "Individual shares" and "Both series" the same way that you interpret the row labeled "Broad indexes".

Observation
I observe that traders use a moving average seeking to see a smoother picture of the pathway price took in the recent past.  I notice that the types of moving averages that traders currently use lag behind the price they get applied to.  I notice when I apply the Time Giant moving average it seems to lead in front of the price it gets applied to.

Problem statement
How can predictive accuracy be observable when securities price patterns are well-reported to lack determinateness? 

Hypothesis
There is a difference between the effects of the Time Giant moving average compared with the effects of other types of moving averages in the population from which the tested securities are drawn.

Designing the experiment
Retrieve 4 price series of broad indexes and 4 of individual shares.
Create a 4-day leading moving average for each price series.
Identify short-term turning points in 4-day leading moving avg.
Randomly assign which index and share receives which treatment.
Treat 2 broad indexes and 2 shares with the MACD formulas.
Treat the other 2 indexes and 2 shares with Time Giant formulas.
Score turning point prediction accuracy using a 21-point scale.
Take the arithmetic mean of scores of both groups.
Use mean scores as the standard for comparing the two indicators.
Display final results.

Data
Drawn from the population of securities are four broad indexes, namely NIKKEI 225, BOVESPA index, Dow Jones Industrial Average, and the Russell 2000.  To represent individual securities Johnson and Johnson, Citibank, T. ROWE PRICE INST AFRICA & ME fund, and Fleetwood Enterprise are chosen. 

I treat (price of) two broad indexes and two securities with the MACD formulas.  I treat the other two indexes and two securities with Time Giant formulas.  Which two indexes get treated by which indicator gets randomly decided.  Same goes for selection of treatment applied to shares. 

I cannot rule out that including a mutual fund in the group labeled individual shares made it easier for Time Giant to achieve a better prediction score on the "individual share" group.  I intentionally included the AFRICA & ME fund in the "individual shares" category.  I wanted a mutual fund category.  This experiment was labor and time intensive and did not allow for the creation of a separate mutual fund category.  Broad indexes, according to
table 1, seem easier to predict by both MACD and Time Giant.  AFRICA & ME fund is a mutual fund.  Mutual funds behave like a broad market index, I believe.  Time Giant score may be higher because an easier to predict mutual is included.  The justification for defining a mutual fund as a single stock is this mutual fund probably contains fewer stocks than the broad indexes contain. 

Readers can consider evidence that Time Giant appears to lead slightly when it is applied to stock of a single company.  See table 2 and table 3 at the bottom of this web page for outcome data of a separate experiment I conducted using the stock of the U.S. company Johnson & Johnson.

The choice of indexes and individual securities to include in this study is not random, but convenient.  I wanted to randomly gather a large number securities from exchanges in all countries.  Restricted access to price data prevented large and random selection.  Time-consuming manual calculations further narrowed the number of securities to a few.  I ended with a total of four (4) broad indexes from three countries: Two indexes (Russell 2000 and Dow Jones) from the U.S., one index (NIKKEI 225) from Japan, and one index (BOVESPA) from Brazil.  I ended with a total of five (5) individual securities from the U.S.

The choice of a "representative" member of the set of traditional moving average-based indicators is convenient not random.  I choose the well-known moving average indicator named the MACD to compare against my Time Giant indicator for this experiment.  I choose the MACD for three reasons: 1) It is widely used, 2) It is the only popular moving average indicator whose formula I can easily find published and 3) It has a formula that is representative of the moving average formula that the vast majority of traders still use today.

Results
See executive summary (listed at the top of this page).

Conclusion
There seems to be a real difference between the effects of the Time Giant and the MACD moving average.  [The results are listed at the top of this page].  Time Giant receives higher and non-negative average scores.  The scores imply that Time Giant moving average makes better descriptions of price movement and may have an ability to lead.  I can infer that differences in scores--similar to these differences--will occur for other financial securities drawn from the same population.

****************************************

The details I list below will not show you how I calculate Time Giant's estimates.  Time Giant's formulas are proprietary. 

The details will show step-by-step how I support my claim that Time Giant leads and not lags.  

Not interested?  OK.

If interested, the remaining paragraphs below show gruesome, gory, gut-bucket details of the method I use to obtain results similar to table 1.  The numbers below, however, come from a separate experiment unrelated to table 1.  The numbers below are not part of the numbers that make
up table 1.

Last chance to detour!

Heavy traffic ahead.  

Not too late to turn back.

Very well.  Let us proceed!

The below tests use only Johnson and Johnson (JNJ) stock market price data to compare prediction accuracy of the MACD and the Time Giant price momentum indicators.

How I score prediction accuracy
I score (price turning-point) prediction accuracy by using this formula.  Prediction Accuracy equals the time period in which the "target zenith" falls minus the time period in which the "prediction zenith" falls.   Its unit of measurement is days, weeks, months, etc.  Zenith is highest part of peak.  Nadir is lowest part of valley.

My first step is write down all the "target dates". 

I locate target dates by 

1) Looking at the "target curve" which is always the orange smooth curve in chart 1 below.  

2) Identifying visually each peak and valley turning point in the smooth orange curve. 

3) Determining exact date of occurrence of the zenith of each peak and the nadir of each valley by manually matching each zenith and peak with one date and one price in their price data set.  Zenith means highest tip of a peak.  Nadir means lowest point of a valley.

4) Recording the date that each zenith and nadir occurs.

Chart 1. Target curve is smooth orange curve labeled 4-day LMA.

See the smooth orange curve above that is labeled "4-day LMA"?  The orange-colored curve is the "target curve".  The 4-day LMA is the "target curve".  There is only one target curve and it is a simple 4-day leading moving average of daily closing prices of Johnson and Johnson (yes I said "leading" moving average).  It can be seen in the bottommost chart of chart 1.     I can see 4 peaks in the 4-day LMA curve.  Each zenith of a peak falls on an exact date.  For instance, the zenith of the four peaks occurs in time periods 158, 170, 179, and 192.  The nadir of the four valleys occurs in time periods 153, 165, 175, and 184. 

I use price data to pinpoint exactly the time period that each zenith falls in, and each nadir falls in.  I use the picture chart graph of the target curve to visually choose major peaks and valleys of the target curve.  The target curve is reality.  Dates of the zenith and nadir OF THE TARGET CURVE are the only targets that get forecast.

Zenith and nadir date are what I call the "target date".  So, I find and write down the target date for every nadir and zenith. 

[TIP #1: ALWAYS SELECT ZENITHS AND NADIRS THAT ALTERNATE.  This is an unshakable rule.  W. D. Gann often selected price turning points that alternate.  Peaks and valleys of many popular moving averages and oscillators like to alternate.  I exclusively study moving averages.  Time Giant is based on moving averages.  Do not make yourself crazy.  Do not make your  analysis difficult.  Alternate your peaks and valleys.

TIP #2: GIVEN A CHOICE, TRY TO SELECT A PEAK AND A VALLEY THAT ARE SEPARATED BY BETWEEN 4 TO 10 TIME PERIODS.  There is a 10-period short-term cycle that shows up in so many financial markets.  Important short-term peaks and valleys are often separated by 4 to 10 time periods.  I  am not the first or only person saying this.  I study short-term price movements.  Time Giant was built to predict short-term price movements.]

I accept target date of 170.  Why?  I accept because a zenith occurs in time period 170 at a price of $59.13 in the 4-day LMA orange colored smooth curve, as seen in chart 1 above.  I verify the 4-day LMA price $59.13 in time period 170 in the long data table 2 listed below.

Formula for accuracy looks like this so far.

          Accuracy       =  Target zenith date - Prediction zenith date

                                =             170          -             

Now I need prediction date.  "Prediction date" is date of zenith in  MACD indicator that is closest to date 170.  The closest zenith  in the MACD occurs in time period 174 (see chart 1 for a curve labeled the "MACD indicator".  Verify date in table 2). 

Now the formula for accuracy becomes 

          Accuracy       =  Target zenith date - Prediction zenith date

                                =             170          -             174

Now I can complete the formula.  

          Accuracy       =  Target zenith date - Prediction zenith date

       -4 (days)          =             170           -             174  

Accuracy is negative 4 days.

So whose formula is this?  It is my formula to describe prediction accuracy.  It reads "Prediction accuracy score equals -4 days which means prediction made by MACD indicator lags behind by 4 time periods".  Accuracy is -4 days because MACD indicator was wrong by 4 days.  MACD thinks that zenith in  LMA curve will occur in time period 174.  Prediction of 174 comes 4 days late, lagged, behind, and after real time period of 170.

We need to repeat the process to score Time Giant's prediction accuracy.  

Time Giant thinks period 169 will be date of target zenith.
The date, 169, is Time Giant's zenith nearest to the target date (see chart 1 above).  In the topmost graph of chart 1,  Time Giant is green-colored curve with diamond markers.  Time Giant created a zenith in period 169.

So Time Giant predicts time period 169 will hold target zenith because Time Giant created its zenith in time period 169.  I can now plug in 169, do subtraction and get a score.

          Accuracy       =  Target zenith date - Prediction zenith date

       +1 (days)          =             170          -             169 

Accuracy is positive 1 days.

Accuracy score for Time Giant's prediction gets interpreted "Real actual Target date remains period 170.  Time Giant predicted a zenith in 4-day LMA curve would occur in time period 169.  Time Giant leads by 1 day.  Its accuracy is +1 days."  Time Giant's prediction is 1 day too early.  Early?  Early means it leads!  Leads is good!  Leads is what we want!  The "+" sign means leads.  The "-" sign means lags.  So "+1" means leads by 1 day.  I use a 21-point scoring scale meaning the highest possible accuracy is +10 (leads by 10 days) and the lowest possible accuracy is -10 (lags by 10 days).  An accuracy score of "0" means neither leads nor lags because the prediction was a direct hit; the prediction zenith date would exactly match the target zenith date.  The 21-point scale on a number line looks like
this: -10 ... 0 ... +10.

Table 2 answers four questions: Does a peak or valley in price series occur?  When does a peak or valley occur? Which moving average leads?  Which moving average lags?  Here is sample of what can be learned from table 2:

Peak in period   170.  Time Giant leads by 1.  MACD  lags by -4.
Valley in period 175.  Time Giant leads by 0.  MACD  lags by -4.
Peak in period   179.  Time Giant lags by  -1. MACD  lags by -4. 
Valley in period  184. Time Giant lags by  -1.  MACD lags by -3.

Table 2 contains all the lead versus lag results for the time period under study namely July 21, 1997 through December 10, 1997 using Johnson and Johnson (JNJ) share prices.

Table 3 RESULTS says the quantity "t" called the "t-statistic" has a value of 5.956. There are 34 degrees of freedom (df).  Table 3 RESULTS also displays mean prediction accuracy scores of Time Giant and MACD which are +0.44 and -2.48, respectively. 

Discussion
There seems to be a real difference between the effects of the Time Giant and the MACD moving average.  Time Giant receives a higher and non-negative prediction score.  The score implies that Time Giant makes better descriptions of price movement and Time Giant may have an ability to lead.  I can infer that Time Giant will lead slightly other price series drawn from the same population of companies as Johnson and Johnson (JNJ).

Three remaining side points
1)    Unit of measurement for the variable named "score" is the same as the time period of my price data series--days, weeks, months, etc.  The variable "score" shows how well the prediction did.

References

The following references are used to write this article.

"Writing Hypotheses: a student lesson",
http://www.accessexcellence.org/LC/TL/filson/writhypo.php

"Formatting Hypotheses",
http://www.accessexcellence.org/LC/TL/filson/formathypo.php

"OneLook Reverse Dictionary",
http://www.onelook.com/reverse-dictionary.shtml

Snedecor and Cochran, Statistical Methods, 8th edition, 1989, Iowa State University Press. 

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Last revised: February 24, 2011.