Henderson Weighted Moving Average

//@version=6
// Copyright (c) 2018-present, Alex Orekhov (everget)
// Henderson Weighted Moving Average script may be freely distributed under the terms of the GPL-3.0 license.
const string MA_SHORT_TITLE = 'HWMA'
indicator('Henderson Weighted Moving Average', shorttitle = MA_SHORT_TITLE, overlay = true, behind_chart = false)

length = input.int(7, minval = 1, title = 'Length')
src = input.source(close, title = 'Source')

var highlightDirectionTooltip = 'Colors the ' + MA_SHORT_TITLE + ' according to its direction:\n• Green = rising\n• Pink = falling'
highlightDirection = input.bool(
     true
     , title = 'Highlight Direction'
     , tooltip = highlightDirectionTooltip
     )

var applyBarColorsTooltip = 'Colors price bars according to the ' + MA_SHORT_TITLE + ' direction:\n• Bullish color = rising ' + MA_SHORT_TITLE + '\n• Bearish color = falling ' + MA_SHORT_TITLE
applyBarColors = input.bool(
     true
     , title = 'Apply Bar Colors'
     , tooltip = applyBarColorsTooltip
     )

var applyBgColorsTooltip = 'Colors the chart background according to the ' + MA_SHORT_TITLE + ' direction:\n• Bullish color = rising ' + MA_SHORT_TITLE + '\n• Bearish color = falling ' + MA_SHORT_TITLE
applyBgColors = input.bool(
     false
     , title = 'Apply Background Colors'
     , tooltip = applyBgColorsTooltip
     )

//---

// The general form of the weights of the (2m + 1)-term Henderson Weighted Moving Average
_hwmaWeight(float m, float j) =>
    m1 = m + 1
    m2 = m + 2
    m3 = m + 3
    powj2 = j * j
    powm22 = m2 * m2

    numerator =
         315 * (m1 * m1 - powj2) *
         (powm22 - powj2) *
         (m3 * m3 - powj2) *
         (3 * powm22 - 11 * powj2 - 16)
    denominator =
         8 * m2 * (powm22 - 1) *
         (4 * powm22 - 1) *
         (4 * powm22 - 9) *
         (4 * powm22 - 25)
    denominator != 0 ? numerator / denominator : 0

// The kernel depends only on `length`, so build it once instead of running the eight-term weight formula for every tap on every bar
var array<float> weights = array.new_float(0)
var float weightSum = 0.0
if array.size(weights) == 0
    termMult = (length - 1) / 2
    for i = 0 to length - 1
        weight = _hwmaWeight(termMult, i - termMult)
        array.push(weights, weight)
        weightSum += weight

sum = 0.0
for i = 0 to length - 1
    sum += nz(src[i], src) * array.get(weights, i)
ma = weightSum != 0 ? sum / weightSum : src

//---

const color bullishColor = #09b71e
const color bearishColor = #e91e63

const color bullishBarColor = color.new(bullishColor, 50)
const color bearishBarColor = color.new(bearishColor, 50)

const color bullishWickColor = bullishColor
const color bearishWickColor = bearishColor

const color bullishBgColor = color.new(bullishColor, 88)
const color bearishBgColor = color.new(bearishColor, 88)

isBullishSlope = ma > ma[1]

maColor = highlightDirection
     ? (isBullishSlope ? bullishColor : bearishColor)
     : #512da8

plot(ma, title = MA_SHORT_TITLE, linewidth = 2, color = maColor)

maBarColor = applyBarColors ? (isBullishSlope ? bullishBarColor : bearishBarColor) : na
maWickColor = applyBarColors ? (isBullishSlope ? bullishWickColor : bearishWickColor) : na
maBgColor = applyBgColors ? (isBullishSlope ? bullishBgColor : bearishBgColor) : na

barcolor(title = 'Bar Color', color = maBarColor)
plotcandle(open, high, low, close, title = 'Bar Color', color = na, wickcolor = maWickColor, bordercolor = na, display = display.pane)
bgcolor(title = 'Background Color', color = maBgColor)

//---

bullishColorChangeAlert = maColor[1] != bullishColor and maColor == bullishColor
bearishColorChangeAlert = maColor[1] != bearishColor and maColor == bearishColor
anyColorChangeAlert = maColor != maColor[1]

alertcondition(bullishColorChangeAlert, title = 'Bullish Color Change', message = MA_SHORT_TITLE + ' - Bullish Color Change\nSymbol: {{exchange}}:{{ticker}}\nPrice: {{close}}')
alertcondition(bearishColorChangeAlert, title = 'Bearish Color Change', message = MA_SHORT_TITLE + ' - Bearish Color Change\nSymbol: {{exchange}}:{{ticker}}\nPrice: {{close}}')
alertcondition(anyColorChangeAlert, title = 'Any Color Change', message = MA_SHORT_TITLE + ' - Any Color Change\nSymbol: {{exchange}}:{{ticker}}\nPrice: {{close}}')