[DMcL] Nadaraya-Watson Kernel

-- original script by jdehorty on tradingview
-- Author: DMcL
EnableHighSpeedUpdates(true)

DefineCommand('Nadaraya_Watson_Kernel', 'Signals long or short when kernel changes bullish/bearish')


-- Parameters

local alpha = DefineParameter(NumberType, 'Alpha', 'NQK Alpha', true, 2)
local h = DefineParameter(NumberType, 'Lookback Window', 'Lookback Window', true, 44)
local r = DefineParameter(NumberType, 'Relative Weighting', 'Relative Weighting', true, 6)
local x_0 = DefineParameter(NumberType, "Start Regression at Bar", "Start Regression at Bar", true, 44)



-- Data
local close = ClosePrices()
local high = HighPrices()
local ohlc = OHLCPrices()
local low = LowPrices()
local smoothColors = Input("Smooth Colors", false)
local lag = Input("Lag", 2)


-- Kernel function

local function kernel_regression (_src, _alpha, _r, _h)
    local _currentWeight = 0
    local _cumulativeWeight = 0
    for i = 1, _alpha + x_0 do
        local y = _src[i]
        local w = Pow( 1 + (Pow(i, 2) / (Pow(_h, 2) * 2 * _r )), -_r)
         _currentWeight = _currentWeight + (y*w)
         _cumulativeWeight = _cumulativeWeight + w
    end
    return  _currentWeight / _cumulativeWeight
end



-- Estimations


local yhat1 = kernel_regression(ohlc, alpha, r, h)
local yhat2 = kernel_regression(ohlc, alpha, r, h - lag)


-- Rates of Change
local wasBearish = yhat1[3] > yhat1[2]
local wasBullish = yhat1[3] < yhat1[2]
local isBearish = yhat1[2] > yhat1[1]
local isBullish = yhat1[2] < yhat1[1]
local isBearishChange = isBearish and wasBullish
local isBullishChange = isBullish and wasBearish

-- Crossovers
local isBullishCross = CrossOver(yhat2[1], yhat1[1])
local isBearishCross = CrossUnder(yhat2[1], yhat1[1]) 
local isBullishSmooth = yhat2[1] > yhat1[1]
local isBearishSmooth = yhat2[1] < yhat1[1]




-- // Alert Variables
local alertBullish = smoothColors and isBullishCross or isBullishChange
local alertBearish = smoothColors and isBearishCross or isBearishChange


-- Plot
local guid = Load("guid",NewGuid())

local green = Load('green', false)
local red = Load('red', false)

if alertBullish then
    green = true
    red = false
    guid = NewGuid()
    Save("guid",guid)
end
if alertBearish then
    green = false
    red = true
    guid = NewGuid()
    Save("guid",guid)
end
    
Save('green', green)
Save('red', red)

if green == true then
    Plot(0, "Bullish Rational Quadratic Kernel Estimate", yhat1, {color=Green, id=guid, width=3})
end
if red == true then
    Plot(0, "Bearish Rational Quadratic Kernel Estimate", yhat1, {color=Red, id=guid, width=3})
end




-- signal
local signal = SignalNone


if alertBullish then 
    signal = SignalLong
    PlotShape(0, ShapeTriangleUp, DarkGreen, 5, false)
end

if alertBearish then 
    signal = SignalShort
    PlotShape(0, ShapeTriangleDown, Red, 5, true)
end


DefineOutput(EnumType, signal)