Pythagorean Means of Moving Averages

2021년 12월 16일

DESCRIPTION
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 = [1/sqrt(2)] = [sqrt(2)/2] = sin 45˚ = cos 45˚.
11. Displaces the plots horizontally +/- by a user defined number of periods.

PURPOSE

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

CREDITS

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.

2021년 12월 18일

릴리즈 노트

1) Added a list of mathematical constants to select as a deviation multiplier.
2) Edited script notes.

2021년 12월 18일

릴리즈 노트

1) updated script notes.
2) removed unrelated indicators from chart.

2021년 12월 18일

릴리즈 노트

1. Updated constants list.

2021년 12월 20일

릴리즈 노트

1. Added selection for period lengths based on either Fibonacci Numbers, Lucas Numbers, or Mersenne primes.

2021년 12월 20일

릴리즈 노트

Updated variable names.

2021년 12월 20일

릴리즈 노트

1. Added additional number sequences.

2021년 12월 21일

릴리즈 노트

Edited script: 1) moving averages periods, 2) new number sequences, 3) new constants.
Added script notes.

2021년 12월 23일

릴리즈 노트

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).

2021년 12월 23일

릴리즈 노트

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.

2021년 12월 26일

릴리즈 노트

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.

2021년 12월 27일

릴리즈 노트

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.

2021년 12월 27일

릴리즈 노트

Added options to plot 2 reference moving averages and displace these +/- horizontally by a specified number of periods.

2021년 12월 29일

릴리즈 노트

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.

2021년 12월 31일

릴리즈 노트

1. Corrected a typo in period lengths
2. Added more reference MAs

2022년 1월 3일

릴리즈 노트

Added Tillson's T3 moving average.

2022년 1월 6일

릴리즈 노트

Added different options for source for the four reference plots

2022년 1월 18일

릴리즈 노트

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.

2022년 1월 18일

릴리즈 노트

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.

2022년 1월 20일

릴리즈 노트

Modified average price calculations

2022년 2월 4일

릴리즈 노트

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.

2022년 2월 10일

릴리즈 노트

Adjusted display of moving averages.

2022년 2월 10일

릴리즈 노트

corrected an error found in previous update

2022년 4월 19일

릴리즈 노트

1) Edited code for plot displacement.
2) Edited notes.

2022년 4월 19일

릴리즈 노트

Edited notes.

2022년 8월 7일

릴리즈 노트

Updated defaults

2023년 7월 11일

릴리즈 노트

Added constants, corrected minor typos.

2023년 7월 11일

릴리즈 노트

Changed defaults and variable names.

2023년 7월 12일

릴리즈 노트

More typos found. These are variable names/descriptions only.

2023년 7월 13일

릴리즈 노트

Edited defaults.

2023년 7월 14일

릴리즈 노트

Found more typos in descriptions.

4월 22일

릴리즈 노트

Edited script notes. Updated chart.