Standardization (Z-score)

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Standardization (Z-score)", "STANDARDIZE", overlay=false, precision=4)

//@function Calculates the Z-score of a series over a lookback period.
//@param src series float Input data series.
//@param len simple int Lookback period for calculating mean and standard deviation (must be > 1 for sample stdev).
//@returns series float The Z-score of the current data point, or na if issues like insufficient data or zero stdev for a non-mean current value.
standardize(series float src, simple int len) =>
    if len <= 1
        float(na)
    var S1 = 0.0
    var S2 = 0.0
    var N = 0
    var float[] window_data_vals = array.new_float(0)
    var bool[]  window_data_is_na = array.new_bool(0)
    float x_new = src[0]
    bool x_new_is_na = na(x_new)
    if array.size(window_data_vals) == len
        float x_old_val = array.get(window_data_vals, 0)
        bool x_old_was_na = array.get(window_data_is_na, 0)
        array.shift(window_data_vals)
        array.shift(window_data_is_na)
        if not x_old_was_na
            S1 -= x_old_val
            S2 -= x_old_val * x_old_val
            N -= 1
    array.push(window_data_vals, x_new_is_na ? 0.0 : x_new)
    array.push(window_data_is_na, x_new_is_na)
    if not x_new_is_na
        S1 += x_new
        S2 += x_new * x_new
        N += 1
    float z_score = na
    if N < 2
        z_score := na
    else
        float mean_val = S1 / N
        float variance_pop = (S2 / N) - (mean_val * mean_val)
        variance_pop := variance_pop < 1e-10 ? 0.0 : variance_pop
        float variance_sample = variance_pop * N / (N - 1)
        float stdev_val = math.sqrt(variance_sample)
        if x_new_is_na
            z_score := na
        else if stdev_val > 1e-10
            z_score := (x_new - mean_val) / stdev_val
        else
            z_score := (math.abs(x_new - mean_val) < 1e-10) ? 0.0 : na
    z_score

// Inputs
i_source = input.source(close, title="Source")
i_length = input.int(20, title="Lookback Period", minval=2, tooltip="Period for mean and standard deviation. Must be at least 2 for stdev.")

// Calculation
z_score_value = standardize(i_source, i_length) // Renamed for clarity

// Plot
plot(z_score_value, "Z-score", color=color.yellow, linewidth=2)
hline(0, "Zero Line", color=color.gray, linestyle=hline.style_dashed)