Autoregressive FIR Moving Average (AFIRMA)

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Autoregressive FIR Moving Average (AFIRMA)", "AFIRMA", overlay=true)

//@function Calculates AFIRMA using various windowing functions with optional least squares cubic spline fitting
//@param source Series to calculate AFIRMA from
//@param period Lookback period - window size
//@param windowType Window function type (1:Hanning, 2:Hamming, 3:Blackman, 4:Blackman-Harris)
//@param leastSquares Apply least squares cubic polynomial fitting for autoregressive prediction
//@returns AFIRMA value, calculates from first bar using available data
//@optimized Uses windowing functions with O(n) complexity; least squares adds O(n) for polynomial fitting
afirma(series float src, simple int period, simple int windowType=4, simple bool leastSquares=false) =>
    float result = src
    if period <= 0
        runtime.error("Period must be greater than 0")
    if windowType < 1 or windowType > 4
        runtime.error("WindowType should be in range [1-4]")
    int p = math.min(bar_index + 1, period)

    if p > 1
        var array<float> coefs = array.new_float(1, 0.0)
        var int prevPeriod = 0
        var int prevWindowType = -1
        if p != prevPeriod or windowType != prevWindowType
            coefs := array.new_float(p, 0.0)
            float a0 = 0.35875
            float a1 = -0.48829
            float a2 = 0.14128
            float a3 = -0.01168
            if windowType == 1
                a0 := 0.50
                a1 := -0.50
            else if windowType == 2
                a0 := 0.54
                a1 := -0.46
            else if windowType == 3
                a0 := 0.42
                a1 := -0.50
                a2 := 0.08
            float TWO_PI = 6.28318530718
            float twoPiDivP = TWO_PI / p
            for k = 0 to p - 1
                float kTwoPiDivP = k * twoPiDivP
                float coef = a0 + a1 * math.cos(kTwoPiDivP)
                if a2 != 0.0
                    coef += a2 * math.cos(2.0 * kTwoPiDivP)
                if a3 != 0.0
                    coef += a3 * math.cos(3.0 * kTwoPiDivP)
                array.set(coefs, k, coef)
            prevPeriod := p
            prevWindowType := windowType
        float sum = 0.0
        float weightSum = 0.0
        int validCount = 0
        for i = 0 to p - 1
            float price = src[i]
            if not na(price)
                float coef = array.get(coefs, i)
                sum += price * coef
                weightSum += coef
                validCount += 1
        result := validCount > 0 and weightSum > 0 ? sum / weightSum : src

        if leastSquares and p > 2
            int n = math.min(math.floor((p - 1) / 2), 50)
            if n >= 2
                var float sx = 0.0
                var float sx2 = 0.0
                var int prevN = 0

                if n != prevN
                    sx := 0.0
                    sx2 := 0.0
                    for i = 0 to n - 1
                        sx += i
                        sx2 += i * i
                    prevN := n

                float sy = 0.0
                float sxy = 0.0
                for i = 0 to n - 1
                    float yi = nz(src[i])
                    sy += yi
                    sxy += i * yi

                float denom = n * sx2 - sx * sx
                if math.abs(denom) > 1e-10
                    float slope = (n * sxy - sx * sy) / denom
                    float intercept = (sy - slope * sx) / n

                    var array<float> fittedBuffer = array.new_float(p, na)
                    for i = 0 to n - 1
                        float fitted = intercept + slope * i
                        array.set(fittedBuffer, i, fitted)

                    float lsSum = 0.0
                    float lsCount = 0.0
                    for i = 0 to p - 1
                        float val = i < n ? array.get(fittedBuffer, i) : nz(src[i])
                        if not na(val)
                            lsSum += val
                            lsCount += 1.0

                    result := lsCount > 0 ? lsSum / lsCount : result
    result

// ---------- Main loop ----------

// Inputs
i_period = input.int(20, "Period", minval=1)
i_source = input.source(close, "Source")
i_windowType = input.int(4, "Window Function", minval=1, maxval=4, tooltip="1:Hanning, 2:Hamming, 3:Blackman, 4:Blackman-Harris")
i_leastSquares = input.bool(false, "Least Squares Method", tooltip="Enable cubic polynomial fitting for autoregressive prediction")

// Calculation
afirma_value = afirma(i_source, i_period, i_windowType, i_leastSquares)

// Plot
plot(afirma_value, "AFIRMA", color=color.yellow, linewidth=2)