Pythagorean Means of Moving Averages

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Pythagorean Means of Moving Averages

1. Calculates a set of moving averages for high, low, close, open and typical prices, each at multiple periods.
Period values follow the Fibonacci sequence.
The "short" set includes moving average having the following periods: 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.
The "mid" set includes moving average having the following periods: 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597.
The "long" set includes moving average having the following periods: 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181.
2. User selects the type of moving average: SMA , EMA , HMA , RMA, WMA , VWMA .
3. Calculates the mean of each set of moving averages.
4. User selects the type of mean to be calculated: 1) arithmetic, 2) geometric, 3) harmonic , 4) quadratic, 5) cubic . Multiple mean calculations may be displayed simultaneously, allowing for comparison.
5. Plots the mean for high, low, close, open, and typical prices.
6. User selects which plots to display: 1) high and low prices, 2) close prices, 3) open prices, and/or 4) typical prices.
7. Calculates and plots a vertical deviation from an origin mean--the mean from which the deviation is measured.
8. Deviation = origin mean x a x b^(x/y)/c.
9. User selects the deviation origin mean: 1) high and low prices plot, 2) close prices plot, or 3) typical prices plot.
10. User defines deviation variables a, b, c, x and y.
Examples of deviation:
a) Percent of the mean = 1.414213562 = 2^(1/2) = Pythagoras's constant (default).
b) Percent of the mean = 0.7071067812 = = = sin 45˚ = cos 45˚.
11. Displaces the plots horizontally +/- by a user defined number of periods.


1. Identify price trends and potential levels of support and resistance .


1. "Fibonacci Moving Average" by Sofien Kaabar: two plots, each an arithmetic mean of EMAs of 1) high prices and 2) low prices, with periods 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181.
2. "Solarized" color scheme by Ethan Schoonover.
1) Added a list of mathematical constants to select as a deviation multiplier.
2) Edited script notes.
1) updated script notes.
2) removed unrelated indicators from chart.
1. Updated constants list.
1. Added selection for period lengths based on either Fibonacci Numbers, Lucas Numbers, or Mersenne primes.
Updated variable names.
1. Added additional number sequences.
Edited script: 1) moving averages periods, 2) new number sequences, 3) new constants.
Added script notes.
1. Added option to calculate double and triple exponential moving averages. Moving average options include: SMA, EMA, DEMA, TEMA, RMA, WMA, VWMA.
2. Chart displayed shows the cubic mean of EMAs having period length values equal to Mersenne prime exponents (3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203).
Added some flexibility in how the plots can be adjusted:
1. increase all moving averages' periods by a specified number of periods.
2. apply the above to high prices or low prices, open prices or close prices, or typical prices.
3. added the OEIS reference number next to the number sequence names within the script notes.
1. Added more number sequences: Pell, Padovan, Perrin, Catalan, Narayana.
2. Added more moving averages: Triple-EMA (TEMA), Quadruple-EMA (QEMA), Quintuple-EMA (PEMA).

Note: TEMA, QEMA, and PEMA may not display when used with "long" or "mid" lookback periods with some number sequences. If TEMA, QEMA, or PEMA do not display, select a shorter lookback period, e.g., "mid" or "short", or a number sequence having fewer periods included within the current lookback selection.
1. Added the option to displace plots horizontally: 1) plots and deviations generated from Open, High, Low, and Close prices separately from 2) plots generated from Typical Prices.
2. Added the Jacobsthal number sequence.
Added options to plot 2 reference moving averages and displace these +/- horizontally by a specified number of periods.
1. Added option to choose Zero Lag Exponential Moving Averages. The selected moving average type is what is used in mean calculations.
2. Fixed error in mean equation script notes. Plotted mean was correct. Notes were incorrect, now corrected.
3. Change optional defaults as follows: Cubic mean of EMAs, with EMA periods equal to the Lucas Numbers. (Lucas numbers are related to Fibonacci numbers in that their ratio is also equal to the Golden Ratio.) Offset from mean of typical price (High + Low + Close) / 3 EMAs equal to 3x the Golden Ratio. Mean of typical prices is shifted forward 29 periods. Optional reference moving averages displayed are 50 and 250 EMA.
1. Corrected a typo in period lengths
2. Added more reference MAs
Added Tillson's T3 moving average.
Added different options for source for the four reference plots
Fixed some errors in the script notes.
Added fill between mean of moving averages sourcing typical prices and the same mean displaced by a specified number of periods.
for mean of moving averages prices source, removed typical and added average which includes typical, mean, and other calculations for average price. User selects the calculation to apply.
Modified average price calculations
Removed the reference moving averages.
Added an option to display or hide all of the moving averages used in the calculation of the mean of moving averages.
Additionally, these moving averages can be translated horizontally by a specified number of periods.
Adjusted display of moving averages.
corrected an error found in previous update
1) Edited code for plot displacement.
2) Edited notes.
Edited notes.
Updated defaults


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