Farey Sequence Weighted Moving Average For ThinkOrSwim

[AlphaOptions]

Author states: A moving average that weighted with Farey fractions. It matches a standard linear weighted average almost one-to-one. Why? Because both averages have strictly monotonic weighting sequences and assign a higher weight to latests data. So, Farey weights are just scaled to [0, 1] linear ones. Instead of specifing period you specify an order of Farey sequence. To learn more about Farey sequence

It is a rather unusual version of a weighted moving average. Once translated, we can make comparisons to others in TOS
Background info on Farey Sequence - https://en.wikipedia.org/wiki/Farey_sequence

Here is the original Tradingview code:
https://www.tradingview.com/script/UQ48Qh3y-Farey-Sequence-Weighted-Moving-Average/

For the new ThinkOrSwim code, you must scroll down to the next post

 

[mashume]

Interesting. I do love interesting mathematical sequences. Thank your for bringing this one to my attention.

# //@version=4
# // Copyright (c) 2019-present, Alex Orekhov (everget)
# // Farey Sequence Weighted Moving Average script may be freely distributed under the terms of the GPL-3.0 license.
# study("Farey Sequence Weighted Moving Average", shorttitle="FSWMA", overlay=true)
# ThinkScript conversion by mashume for UseThinkScript
input plot_type = {default "5", "2","3","4","6","7","8","9","10","11","12","13","14"};

def src = close;

def src1 = src[1];
def src2 = src[2];
def src3 = src[3];
def src4 = src[4];
def src5 = src[5];
def src6 = src[6];
def src7 = src[7];
def src8 = src[8];
def src9 = src[9];
def src10 = src[10];
def src11 = src[11];
def src12 = src[12];
def src13 = src[13];
def src14 = src[14];
def src15 = src[15];
def src16 = src[16];
def src17 = src[17];
def src18 = src[18];
def src19 = src[19];
def src20 = src[20];
def src21 = src[21];
def src22 = src[22];
def src23 = src[23];
def src24 = src[24];
def src25 = src[25];
def src26 = src[26];
def src27 = src[27];
def src28 = src[28];
def src29 = src[29];
def src30 = src[30];
def src31 = src[31];
def src32 = src[32];
def src33 = src[33];
def src34 = src[34];
def src35 = src[35];
def src36 = src[36];
def src37 = src[37];
def src38 = src[38];
def src39 = src[39];
def src40 = src[40];
def src41 = src[41];
def src42 = src[42];
def src43 = src[43];
def src44 = src[44];
def src45 = src[45];
def src46 = src[46];
def src47 = src[47];
def src48 = src[48];
def src49 = src[49];
def src50 = src[50];
def src51 = src[51];
def src52 = src[52];
def src53 = src[53];
def src54 = src[54];
def src55 = src[55];
def src56 = src[56];
def src57 = src[57];
def src58 = src[58];
def src59 = src[59];
def src60 = src[60];
def src61 = src[61];
def src62 = src[62];
def src63 = src[63];

plot Avg;
Avg.SetDefaultColor(color.dark_orange);
Avg.SetLineWeight(2);
switch (plot_type) {
case "2":
    Avg = (src + 0.5 * src1) / 1.5;
case "3":
    Avg = (src + 0.667 * src1 + 0.5 * src2 + 0.333 * src3) / 2.5;
case "4":
    Avg = (src + 0.75 * src1 + 0.667 * src2 + 0.5 * src3 + 0.333 * src4 + 0.25 * src5) / 3.5;
case "5":
    Avg = (src + 0.8 * src1 + 0.75 * src2 + 0.667 * src3 + 0.6 * src4 + 0.5 * src5 + 0.4 * src6 + 0.333 * src7 + 0.25 * src8 + 0.2 * src9) / 5.5;
case "6":
    Avg = (src + 0.833 * src1 + 0.8 * src2 + 0.75 * src3 + 0.667 * src4 + 0.6 * src5 + 0.5 * src6 + 0.4 * src7 + 0.333 * src8 + 0.25 * src9 + 0.2 * src10 + 0.167 * src11) / 6.5;
case "7":
    Avg = (src + 0.857 * src1 + 0.833 * src2 + 0.8 * src3 + 0.75 * src4 + 0.714 * src5 + 0.667 * src6 + 0.6 * src7 + 0.571 * src8 + 0.5 * src9 + 0.429 * src10 + 0.4 * src11 + 0.333 * src12 + 0.286 * src13 + 0.25 * src14 + 0.2 * src15 + 0.167 * src16 + 0.143 * src17) / 9.5;
case "8":
    Avg = (src + 0.875 * src1 + 0.857 * src2 + 0.833 * src3 + 0.8 * src4 + 0.75 * src5 + 0.714 * src6 + 0.667 * src7 + 0.625 * src8 + 0.6 * src9 + 0.571 * src10 + 0.5 * src11 + 0.429 * src12 + 0.4 * src13 + 0.375 * src14 + 0.333 * src15 + 0.286 * src16 + 0.25 * src17 + 0.2 * src18 + 0.167 * src19 + 0.143 * src20 + 0.125 * src21) / 11.5;
case "9":
    Avg = (src + 0.889 * src1 + 0.875 * src2 + 0.857 * src3 + 0.833 * src4 + 0.8 * src5 + 0.778 * src6 + 0.75 * src7 + 0.714 * src8 + 0.667 * src9 + 0.625 * src10 + 0.6 * src11 + 0.571 * src12 + 0.556 * src13 + 0.5 * src14 + 0.444 * src15 + 0.429 * src16 + 0.4 * src17 + 0.375 * src18 + 0.333 * src19 + 0.286 * src20 + 0.25 * src21 + 0.222 * src22 + 0.2 * src23 + 0.167 * src24 + 0.143 * src25 + 0.125 * src26 + 0.111 * src27) / 14.5;
case "10":
    Avg = (src + 0.9 * src1 + 0.889 * src2 + 0.875 * src3 + 0.857 * src4 + 0.833 * src5 + 0.8 * src6 + 0.778 * src7 + 0.75 * src8 + 0.714 * src9 + 0.7 * src10 + 0.667 * src11 + 0.625 * src12 + 0.6 * src13 + 0.571 * src14 + 0.556 * src15 + 0.5 * src16 + 0.444 * src17 + 0.429 * src18 + 0.4 * src19 + 0.375 * src20 + 0.333 * src21 + 0.3 * src22 + 0.286 * src23 + 0.25 * src24 + 0.222 * src25 + 0.2 * src26 + 0.167 * src27 + 0.143 * src28 + 0.125 * src29 + 0.111 * src30 + 0.1 * src31) / 16.5;
case "11":
    Avg = (src + 0.909 * src1 + 0.9 * src2 + 0.889 * src3 + 0.875 * src4 + 0.857 * src5 + 0.833 * src6 + 0.818 * src7 + 0.8 * src8 + 0.778 * src9 + 0.75 * src10 + 0.727 * src11 + 0.714 * src12 + 0.7 * src13 + 0.667 * src14 + 0.636 * src15 + 0.625 * src16 + 0.6 * src17 + 0.571 * src18 + 0.556 * src19 + 0.545 * src20 + 0.5 * src21 + 0.455 * src22 + 0.444 * src23 + 0.429 * src24 + 0.4 * src25 + 0.375 * src26 + 0.364 * src27 + 0.333 * src28 + 0.3 * src29 + 0.286 * src30 + 0.273 * src31 + 0.25 * src32 + 0.222 * src33 + 0.2 * src34 + 0.182 * src35 + 0.167 * src36 + 0.143 * src37 + 0.125 * src38 + 0.111 * src39 + 0.1 * src40 + 0.091 * src41) / 21.5;
case "12":
    Avg = (src + 0.917 * src1 + 0.909 * src2 + 0.9 * src3 + 0.889 * src4 + 0.875 * src5 + 0.857 * src6 + 0.833 * src7 + 0.818 * src8 + 0.8 * src9 + 0.778 * src10 + 0.75 * src11 + 0.727 * src12 + 0.714 * src13 + 0.7 * src14 + 0.667 * src15 + 0.636 * src16 + 0.625 * src17 + 0.6 * src18 + 0.583 * src19 + 0.571 * src20 + 0.556 * src21 + 0.545 * src22 + 0.5 * src23 + 0.455 * src24 + 0.444 * src25 + 0.429 * src26 + 0.417 * src27 + 0.4 * src28 + 0.375 * src29 + 0.364 * src30 + 0.333 * src31 + 0.3 * src32 + 0.286 * src33 + 0.273 * src34 + 0.25 * src35 + 0.222 * src36 + 0.2 * src37 + 0.182 * src38 + 0.167 * src39 + 0.143 * src40 + 0.125 * src41 + 0.111 * src42 + 0.1 * src43 + 0.091 * src44 + 0.083 * src45) / 23.5;
case "13":
    Avg = (src + 0.923 * src1 + 0.917 * src2 + 0.909 * src3 + 0.9 * src4 + 0.889 * src5 + 0.875 * src6 + 0.857 * src7 + 0.846 * src8 + 0.833 * src9 + 0.818 * src10 + 0.8 * src11 + 0.778 * src12 + 0.769 * src13 + 0.75 * src14 + 0.727 * src15 + 0.714 * src16 + 0.7 * src17 + 0.692 * src18 + 0.667 * src19 + 0.636 * src20 + 0.625 * src21 + 0.615 * src22 + 0.6 * src23 + 0.583 * src24 + 0.571 * src25 + 0.556 * src26 + 0.545 * src27 + 0.538 * src28 + 0.5 * src29 + 0.462 * src30 + 0.455 * src31 + 0.444 * src32 + 0.429 * src33 + 0.417 * src34 + 0.4 * src35 + 0.385 * src36 + 0.375 * src37 + 0.364 * src38 + 0.333 * src39 + 0.308 * src40 + 0.3 * src41 + 0.286 * src42 + 0.273 * src43 + 0.25 * src44 + 0.231 * src45 + 0.222 * src46 + 0.2 * src47 + 0.182 * src48 + 0.167 * src49 + 0.154 * src50 + 0.143 * src51 + 0.125 * src52 + 0.111 * src53 + 0.1 * src54 + 0.091 * src55 + 0.083 * src56 + 0.077 * src57) / 29.5;
case "14":
    Avg = (src + 0.929 * src1 + 0.923 * src2 + 0.917 * src3 + 0.909 * src4 + 0.9 * src5 + 0.889 * src6 + 0.875 * src7 + 0.857 * src8 + 0.846 * src9 + 0.833 * src10 + 0.818 * src11 + 0.8 * src12 + 0.786 * src13 + 0.778 * src14 + 0.769 * src15 + 0.75 * src16 + 0.727 * src17 + 0.714 * src18 + 0.7 * src19 + 0.692 * src20 + 0.667 * src21 + 0.643 * src22 + 0.636 * src23 + 0.625 * src24 + 0.615 * src25 + 0.6 * src26 + 0.583 * src27 + 0.571 * src28 + 0.556 * src29 + 0.545 * src30 + 0.538 * src31 + 0.5 * src32 + 0.462 * src33 + 0.455 * src34 + 0.444 * src35 + 0.429 * src36 + 0.417 * src37 + 0.4 * src38 + 0.385 * src39 + 0.375 * src40 + 0.364 * src41 + 0.357 * src42 + 0.333 * src43 + 0.308 * src44 + 0.3 * src45 + 0.286 * src46 + 0.273 * src47 + 0.25 * src48 + 0.231 * src49 + 0.222 * src50 + 0.214 * src51 + 0.2 * src52 + 0.182 * src53 + 0.167 * src54 + 0.154 * src55 + 0.143 * src56 + 0.125 * src57 + 0.111 * src58 + 0.1 * src59 + 0.091 * src60 + 0.083 * src61 + 0.077 * src62 + 0.071 * src63) / 32.5;
  
}

 

[MerryDay]

Thank you @mashume. Great Script!

It is a rather unusual version of a weighted moving average. Once translated, we can make comparisons to others in TOS

So here is the first of the comparisons that you requested.

I added the below code snippet to the bottom of your study.
It would seem to highlight that the farey sequence provides the same transitions as the Heiken-Ashi Trend. Yes?

plot sigUP = if isnan(close) then double.NaN else open[1]<avg[1] and close[1]<avg[1] and close>avg;
sigUP.SetPaintingStrategy(PaintingStrategy.BOOLEAN_ARROW_UP);
sigUP.SetDefaultColor(color.yellow);
sigUP.SetLineWeight(3);

plot sigDN = if isnan(close) then double.NaN else open[1]>avg[1] and close[1]>avg[1] and close<avg;
sigDN .SetPaintingStrategy(PaintingStrategy.BOOLEAN_ARROW_DOWN);
sigDN .SetDefaultColor(color.red);
sigDN .SetLineWeight(2);

 

[mashume]

Looking at this after a cup of coffee, I wonder if all of the "-1" should be in there. I'm afraid I should probably remove them as they were a bit of a kludge and I note that this means duplicated data will be used in the calculations later (as src with no number does get used)... hmmm.

mashume


EDIT:

I removed the extraneous -1s from the code. It seems this is now correct. @MerryDay you may want to re-run your comparison to the HA candles above now that the code is corrected.