Bayesian BBSMA + nQQE Oscillator

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// Bayesian BBSMA: https://www.tradingview.com/v/8lXcviYm/
// nQQE: https://www.tradingview.com/v/CfCuUCeE/

//@version=4
study("Bayesian BBSMA + nQQE Oscillator", shorttitle="Bayesian/nQQE osc", precision=4)

rescale(_src, _oldMin, _oldMax, _newMin, _newMax) =>
    // Rescales series with known min/max.
    // _src            : series to rescale.
    // _oldMin, _oldMax: min/max values of series to rescale.
    // _newMin, _newMin: min/max values of rescaled series.
    _newMin + (_newMax - _newMin) * (_src - _oldMin) / max(_oldMax - _oldMin, 10e-10)


//#################### Bayesian BBSMA

bbSmaPeriod = input(20, title="BB SMA Period", group="═════ Bayesian BBSMA settings ═════")
bbStdDevMult = input(2.5, title="BB Standard Deviation", maxval=50.0)

bbBasis = sma(close, bbSmaPeriod)
bbStdDev = bbStdDevMult * stdev(close, bbSmaPeriod)

bbUpper = bbBasis + bbStdDev
bbLower = bbBasis - bbStdDev

// AO
aoFast = input(5, "AO Fast EMA Length")
aoSlow = input(34, "AO Slow EMA Length")
ao = sma(hl2, aoFast) - sma(hl2, aoSlow)
colorAo = change(ao) > 0 ? color.green : color.red

// AC
acFast = input(5, "AC Fast SMA Length")
acSlow = input(34, "AC Slow SMA Length")
xSMA1_hl2 = sma(hl2, acFast)
xSMA2_hl2 = sma(hl2, acSlow)
xSMA1_SMA2 = xSMA1_hl2 - xSMA2_hl2
xSMA_hl2 = sma(xSMA1_SMA2, acFast)
ac =  xSMA1_SMA2 - xSMA_hl2
cClr = ac > ac[1] ? color.blue : color.red

acAo = (ac + ao) / 2

maAcAoPeriod = input(13, "AC AO MA Period")
showMaAcAo = input(false, "Show AC AO MA?")
maAcAo = vwma(acAo, maAcAoPeriod)

// Combine AC & AO
acIsBlue = ac > ac[1]
acIsRed = not (ac > ac[1])
aoIsGreen = change(ao) > 0
aoIsRed = not (change(ao) > 0)
acAoIsBullish = acIsBlue and aoIsGreen
acAoIsBearish = acIsRed and acIsRed
acAoColorIndex = acAoIsBullish ? 1 : acAoIsBearish ? -1 : 0

// Alligator
smma(src, length) =>
    smma = 0.0
    smma := na(smma[1]) ? sma(src, length) : (smma[1] * (length - 1) + src) / length
lipsLength  = input(title="🐲 Lips Length", defval=5)
teethLength = input(title="🐲 Teeth Length", defval=8)
jawLength   = input(title="🐲 Jaw Length", defval=13)
lipsOffset  = input(title="🐲 Lips Offset", defval=3)
teethOffset = input(title="🐲 Teeth Offset", defval=5)
jawOffset   = input(title="🐲 Jaw Offset", defval=8)
lips        = smma(hl2, lipsLength)
teeth       = smma(hl2, teethLength)
jaw         = smma(hl2, jawLength)

// SMA
smaPeriod = input(20, title="SMA Period")
smaValues = sma(close, smaPeriod)


// Bayesian Theorem Starts
bayesPeriod = input(20, title="Bayesian Lookback Period")

// Next candles are breaking Down
probBbUpperUpSeq = close > bbUpper ? 1 : 0
probBbUpperUp = sum(probBbUpperUpSeq, bayesPeriod) / bayesPeriod
probBbUpperDownSeq = close < bbUpper ? 1 : 0
probBbUpperDown = sum(probBbUpperDownSeq, bayesPeriod) / bayesPeriod

probUpBbUpper = probBbUpperUp / (probBbUpperUp + probBbUpperDown)

probBbBasisUpSeq = close > bbBasis ? 1 : 0
probBbBasisUp = sum(probBbBasisUpSeq, bayesPeriod) / bayesPeriod
probBbBasisDownSeq = close < bbBasis ? 1 : 0
probBbBasisDown = sum(probBbBasisDownSeq, bayesPeriod) / bayesPeriod

probUpBbBasis = probBbBasisUp / (probBbBasisUp + probBbBasisDown)

probSmaUpSeq = close > smaValues ? 1 : 0
probSmaUp = sum(probSmaUpSeq, bayesPeriod) / bayesPeriod
probSmaDownSeq = close < smaValues ? 1 : 0
probSmaDown = sum(probSmaDownSeq, bayesPeriod) / bayesPeriod

probUpSma = probSmaUp / (probSmaUp + probSmaDown)

sigmaProbsDown = nz(probUpBbUpper * probUpBbBasis * probUpSma / probUpBbUpper * probUpBbBasis * probUpSma + ((1 - probUpBbUpper) * (1 - probUpBbBasis) * (1 - probUpSma)))

// Next candles are breaking Up
probDownBbUpper = probBbUpperDown / (probBbUpperDown + probBbUpperUp)
probDownBbBasis = probBbBasisDown / (probBbBasisDown + probBbBasisUp)
probDownSma = probSmaDown / (probSmaDown + probSmaUp)

sigmaProbsUp = nz(probDownBbUpper * probDownBbBasis * probDownSma / probDownBbUpper * probDownBbBasis * probDownSma + ( (1 - probDownBbUpper) * (1 - probDownBbBasis) * (1 - probDownSma) ))

showNextCandleDown = input(true, title="Plot Next Candles Breaking Down?")
plot(showNextCandleDown ? rescale(sigmaProbsDown * 100,0,100,0,60) : na, title="Next Candle Breaking Down Probs", style=plot.style_area, transp=60, color=color.red, linewidth=2)

showNextCandleUp = input(true, title="Plot Next Candles Breaking Up?")
plot(showNextCandleUp ? rescale(sigmaProbsUp * 100,0,100,0,60) : na, title="Next Candle Breaking Up Probs", style=plot.style_area,transp=60, color=color.green, linewidth=2)

probPrime = nz(sigmaProbsDown * sigmaProbsUp / sigmaProbsDown * sigmaProbsUp + ( (1 - sigmaProbsDown) * (1 - sigmaProbsUp) ))

showPrime = input(true, title="Plot Prime Probability?")
plot(showPrime ? rescale(probPrime * 100,0,100,0,60) : na, title="Prime Probability", style=plot.style_area,transp=60, color=color.blue, linewidth=2)

lowerThreshold = input(15.0, title="Lower Threshold")

sideways = probPrime < lowerThreshold / 100 and sigmaProbsUp < lowerThreshold / 100 and sigmaProbsDown < lowerThreshold / 100

longUsingProbPrime = probPrime > lowerThreshold / 100 and probPrime[1] == 0
longUsingSigmaProbsUp = sigmaProbsUp < 1 and sigmaProbsUp[1] == 1

shortUsingProbPrime = probPrime == 0 and probPrime[1] > lowerThreshold / 100
shortUsingSigmaProbsDown = sigmaProbsDown < 1 and sigmaProbsDown[1] == 1

milanIsRed = acAoColorIndex == -1
milanIsGreen = acAoColorIndex == 1
pricesAreMovingAwayUpFromAlligator = close > jaw and open > jaw
pricesAreMovingAwayDownFromAlligator = close < jaw and open < jaw

useBWConfirmation = input(false, title="Use Bill Williams indicators for confirmation?")

bwConfirmationUp = useBWConfirmation ? milanIsGreen and pricesAreMovingAwayUpFromAlligator : true
bwConfirmationDown = useBWConfirmation ? milanIsRed and pricesAreMovingAwayDownFromAlligator : true

longSignal = bwConfirmationUp and (longUsingProbPrime or longUsingSigmaProbsUp)
shortSignal = bwConfirmationDown and (shortUsingProbPrime or shortUsingSigmaProbsDown)

barcolor(longSignal ? color.lime : na, title="Long Bars")
barcolor(shortSignal ? color.maroon : na, title="Short Bars")

//hzl3 = hline(lowerThreshold, color=#333333, linestyle=hline.style_solid)
//hzl4 = hline(0, color=#333333, linestyle=hline.style_solid)
//fill(hzl3, hzl4, title="Lower Threshold", color=sideways ? color.gray : color.maroon, transp=70)

alertcondition(longSignal, title="Long!", message="Bayesian BBSMA - LONG - {{exchange}}:{{ticker}} at {{close}}")
alertcondition(shortSignal, title="Short!", message="Bayesian BBSMA - SHORT - {{exchange}}:{{ticker}} at {{close}}")


//#################### nQQE

src=input(close)
length = input(14,"RSI Length", minval=1, group="═════ nQQE settings ═════")
SSF=input(5, "SF RSI SMoothing Factor", minval=1)
showsignals = input(title="Show Crossing Signals?", type=input.bool, defval=false)
RSII=ema(rsi(src,length),SSF)
TR=abs(RSII-RSII[1])
wwalpha = 1/ length
WWMA = 0.0
WWMA := wwalpha*TR + (1-wwalpha)*nz(WWMA[1])
ATRRSI=0.0
ATRRSI := wwalpha*WWMA + (1-wwalpha)*nz(ATRRSI[1])
QQEF=ema(rsi(src,length),SSF)
QUP=QQEF+ATRRSI*4.236
QDN=QQEF-ATRRSI*4.236
QQES=0.0
QQES:=QUP<nz(QQES[1]) ? QUP : QQEF>nz(QQES[1]) and QQEF[1]<nz(QQES[1]) ? QDN :  QDN>nz(QQES[1]) ? QDN : QQEF<nz(QQES[1]) and QQEF[1]>nz(QQES[1]) ? QUP : nz(QQES[1])
Colorh = QQEF-25>35 ? color.lime : QQEF-25<15 ? color.red : #E8E81A
QQF=plot(QQEF-25,"FAST",color=color.maroon,linewidth=2)
plot(QQEF-25,color=Colorh,linewidth=2)
QQS=plot(QQES-25,"SLOW",color=color.yellow, linewidth=2)
hline(35,color=color.gray,linestyle=2)
hline(15,color=color.gray,linestyle=2)
buySignalr = crossover(QQEF, QQES)
plotshape(buySignalr and showsignals ? (QQES-25)*0.995 : na, title="Buy", text="Buy", location=location.absolute, style=shape.labelup, size=size.tiny, color=color.black, textcolor=color.white, transp=50)
sellSignallr = crossunder(QQEF, QQES)
plotshape(sellSignallr and showsignals ? (QQES-25)*1.005 : na, title="Sell", text="Sell", location=location.absolute, style=shape.labeldown, size=size.tiny, color=color.black, textcolor=color.white, transp=50)
alertcondition(cross(QQEF, QQES), title="Cross Alert", message="QQE Crossing Signal!")
alertcondition(crossover(QQEF, QQES), title="Crossover Alarm", message="QQE BUY SIGNAL!")
alertcondition(crossunder(QQEF, QQES), title="Crossunder Alarm", message="QQE SELL SIGNAL!")
alertcondition(crossover(QQEF, 50), title="Cross 0 Up Alert", message="QQE FAST Crossing 0 UP!")
alertcondition(crossunder(QQEF, 50), title="Cross 0 Down Alert", message="QQE FAST Crossing 0 DOWN!")
alertcondition(crossover(QQEF, 60), title="Cross 10 Up Alert", message="QQE Above 10 UPTREND SIGNAL!")
alertcondition(crossunder(QQEF, 40), title="Cross -10 Down Alert", message="QQE Below -10 DOWNTREND SIGNAL!")
alertcondition(crossunder(QQEF, 60) or crossover(QQEF, 40), title="SIDEWAYS", message="QQE Entering Sideways Market!")


//end of this part


//----- User inputs ---------------------
Lookback1 = input(title="Lookback Left", type=input.integer, defval=56, minval=1)
Lookback2 = input(title="Lookback Right", type=input.integer, defval=0, minval=0)
VertLR = input(title="Show Vertical Left/Right", type=input.bool, defval=true)
VertHL = input(title="Show Vertical Highest/Lowest", type=input.bool, defval=true)
Count = input(title="Show Counts", type=input.bool, defval=true)
FullCount = input(title="Count All Bars", type=input.bool, defval=false)
Fibs = input(title="Show Fib Retrace Lines", type=input.bool, defval=false)
FibsExtHigh = input(title="Show Fib Ext Highs", type=input.bool, defval=false)
FibsExtLow = input(title="Show Fib Ext Lows", type=input.bool, defval=false)


//----- Main ---------------------
// Get left and right endpoints. Though user input says "left" and "right", they are interchangeable.
//   The larger number is left, smaller number right.
left = max(Lookback1, Lookback2)
right = min(Lookback1, Lookback2)
// Total num bars. Must be > 0 for highest() and lowest() to work. Add 1 to left bar, if needed.
left := left - right == 0 ? left + 1 : left
lengthHL = left - right

// Highest price, looking back between the left/right endpoints
highBack = highest(high[right], lengthHL)
// Get # of bars back from present bar (offset).
//   NOTE: highestbars() returns a negative integer. Thus, subtract the right endpoint to get
//         offset from present (right-edge) bar
highOffset = highestbars(high[right], lengthHL) - right

// Lowest price, looking back
lowBack = lowest(low[right], lengthHL)
lowOffset = lowestbars(low[right], lengthHL) - right

// Create a series of timestamps per bar. Needed to determine which bars are at the right edge,
//   While "n" starts at zero (left-edge bar) and counts up to the right-edge bar, this timestamp
//   (or tick) series counts the other way: max value at the left-edge, counting down to zero
//   at the right-edge.
// This tick series is only valid while the indicator loads because "timenow" is the timestamp
//   of loading and "time" is the timestamp of a bar. The difference between the two timestamps
//   shrinks to zero as the righ-edge bar is processed. After loading, "timenow" and "time" are
//   the same value. Thus, "tick" always equals zero as new bars appear. But, for this indicator
//   this is sufficient behavior...
tick = round((timenow - time) / change(time))  // Each bar is a tick (float) in the timeline
// Make a boolean mask for bars between left and right endpoints
mask = FullCount ? true : tick < left and tick >= right ? true : false
// Determine the value of n at the left endpoint, used for visual counts of bars in mask
nOffset = float(na)
nOffset := FullCount ? 0 : tick == left ? bar_index : nz(nOffset[1])

// Note: It would be nice to count between the highest/lowest bars, instead of left/right bars,
//       but this isn't possible because highOffset and lowOffset are moving around as the
//       indicator loads. Thus, "mask" isn't accurate...

//---- Plotting ---------------------
// Horizontal Lines: Highest, Lowest dynamic lines
//   Params trackprice and offset make the horizontal line dynamic, adjusting to new highs/lows
plot(highBack, title="Highest", color=color.red, linewidth=2, trackprice=true, offset=-9999)
plot(lowBack, title="Lowest", color=color.green, linewidth=2, trackprice=true, offset=-9999)

// Veritcal Lines
// Use barstate to paint/re-paint vertical lines, as new bars come into the data set.
//   islast - True for right most bar in data set. Use this to paint vertical bar, then push it back
//       in time with the offset parameter.
//   isrealtime - False while indicator loads. True for the right most bar, after loading.
//   isconfirmed - False while bar is not closed. True when close price appears.
//   isrealtime and isconfirmed - While indicator loads, ignore isconfirmed. After loading, isconfirmed
//       turns off the vertical line, as the bar closes. The next (new) bar is painted. This keeps
//       the vertical bar moving forward, as new bars appear, erasing the old (previous) vertical bar.
VertLRShow = VertLR ? barstate.isrealtime and barstate.isconfirmed ? false :
   barstate.islast ? true : false : false
// Can't use plot() with histogram/column because histbase can't accept "series" values
bgcolor(VertLRShow ? color.gray : na, title="Vertical Left", transp=60, offset=-left + 1)
bgcolor(VertLRShow ? color.gray : na, title="Vertical Right", transp=60, offset=-right)
// Show vertical highest/lowest lines?
VertHLShow = VertHL ? barstate.isrealtime and barstate.isconfirmed ? false :
   barstate.islast ? true : false : false
bgcolor(VertHLShow ? color.red : na, title="Vertical Highest", transp=60, offset=highOffset)
bgcolor(VertHLShow ? color.green : na, title="Vertical Lowest", transp=60, offset=lowOffset)

// Fib levels extension and retracement
priceRange = highBack - lowBack
plot(FibsExtHigh ? lowBack + 3.618 * priceRange : na, title="3.618", color=color.lime, linewidth=2, trackprice=true, offset=-9999)
plot(FibsExtHigh ? lowBack + 2.618 * priceRange : na, title="2.618", color=color.lime, linewidth=2, trackprice=true, offset=-9999)
plot(FibsExtHigh ? lowBack + 1.618 * priceRange : na, title="1.618", color=color.lime, linewidth=2, trackprice=true, offset=-9999)
plot(FibsExtHigh ? lowBack + 1.1 * priceRange : na, color=#88888800, trackprice=true, offset=-9999, editable=false)  // invisible line to work around pine plot bug
plot(Fibs ? lowBack + 1.1 * priceRange : na, color=#88888800, trackprice=true, offset=-9999, editable=false)  // invisible line to work around pine plot bug
plot(Fibs ? lowBack + 0.786 * priceRange : na, title="0.786", color=color.aqua, linewidth=1, trackprice=true, offset=-9999)
plot(Fibs ? lowBack + 0.618 * priceRange : na, title="0.618", color=color.orange, linewidth=2, trackprice=true, offset=-9999)
plot(Fibs ? lowBack + 0.50 * priceRange : na, title="0.5", color=color.yellow, linewidth=2, trackprice=true, offset=-9999)
plot(Fibs ? lowBack + 0.382 * priceRange : na, title="0.382", color=color.orange, linewidth=2, trackprice=true, offset=-9999)
plot(Fibs ? lowBack + 0.236 * priceRange : na, title="0.236", color=color.aqua, linewidth=1, trackprice=true, offset=-9999)
plot(Fibs ? highBack - 1.1 * priceRange : na, color=#88888800, trackprice=true, offset=-9999, editable=false)  // invisible line to work around pine plot bug
plot(FibsExtLow ? highBack - 1.1 * priceRange : na, color=#88888800, trackprice=true, offset=-9999, editable=false)  // invisible line to work around pine plot bug
plot(FibsExtLow ? highBack - 1.618 * priceRange : na, title="1.618", color=color.fuchsia, linewidth=2, trackprice=true, offset=-9999)
plot(FibsExtLow ? highBack - 2.618 * priceRange : na, title="2.618", color=color.fuchsia, linewidth=2, trackprice=true, offset=-9999)
plot(FibsExtLow ? highBack - 3.618 * priceRange : na, title="3.618", color=color.fuchsia, linewidth=2, trackprice=true, offset=-9999)

// Lookback bar count
countMod = mask ? (bar_index - nOffset) % 10 : na
countInt = mask ? floor((bar_index - nOffset) / 10) % 10 : na
plotshape(Count and countMod != 0 ? true : na, style=shape.circle, text="-", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 0 ? true : na, style=shape.circle, text="0", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 1 ? true : na, style=shape.circle, text="1", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 2 ? true : na, style=shape.circle, text="2", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 3 ? true : na, style=shape.circle, text="3", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 4 ? true : na, style=shape.circle, text="4", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 5 ? true : na, style=shape.circle, text="5", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 6 ? true : na, style=shape.circle, text="6", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 7 ? true : na, style=shape.circle, text="7", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 8 ? true : na, style=shape.circle, text="8", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)
plotshape(Count and countMod == 0 and countInt == 9 ? true : na, style=shape.circle, text="9", textcolor=color.gray, color=#88888800, location=location.bottom, size=size.auto, editable=false)


//end of this part