Convolution Moving Average (CONV)

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Convolution Moving Average (CONV)", "CONV", overlay=true)

//@function Calculates a convolution MA using any custom kernel
//@param source Series to calculate CONV from
//@param kernel Array of weights to use as convolution kernel
//@returns CONV value, calculates from first bar using available data
//@optimized Uses custom kernel convolution with O(n) complexity per bar due to lookback loop
conv(series float source, simple array<float> kernel) =>
    int kernel_size = array.size(kernel)
    if kernel_size <= 0
        runtime.error("Kernel must not be empty")
    var array<float> norm_kernel = array.new_float(1, 1.0)
    var int last_kernel_size = 1
    if last_kernel_size != kernel_size
        norm_kernel := array.copy(kernel)
        float kernel_sum = 0.0
        for i = 0 to kernel_size - 1
            kernel_sum += array.get(kernel, i)
        if kernel_sum != 0.0
            float inv_sum = 1.0 / kernel_sum
            for i = 0 to kernel_size - 1
                array.set(norm_kernel, i, array.get(kernel, i) * inv_sum)
        last_kernel_size := kernel_size
    int p = math.min(bar_index + 1, kernel_size)
    float sum = 0.0
    float weight_sum = 0.0
    for i = 0 to p - 1
        float price = source[i]
        if not na(price)
            float w = array.get(norm_kernel, i)
            sum += price * w
            weight_sum += w
    nz(sum / weight_sum, source)

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

// Inputs
i_source = input.source(close, "Source")
i_kernel = array.from(1.0, 2.5, -3.14, 0.0, 1.0)

// Calculation
conv_value = conv(i_source, i_kernel)

// Plot
plot(conv_value, "CONV", color=color.yellow, linewidth=2)