Cointegration

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Cointegration (COINTEGRATION)", "COINTEGRATION", overlay=false)

sma(series float source, simple int period) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    var int p = period
    var array<float> buffer = array.new_float(p, na)
    var int head = 0
    var float sum = 0.0
    var int valid_count = 0
    float oldest = array.get(buffer, head)
    if not na(oldest)
        sum -= oldest
        valid_count -= 1
    if not na(source)
        sum += source
        valid_count += 1
    array.set(buffer, head, source)
    head := (head + 1) % p
    nz(sum / valid_count, source)

stddev(series float src, int len) =>
    if len <= 0
        runtime.error("Period must be greater than 0")
    var int p = math.max(1, len)
    var array<float> buffer = array.new_float(p, na)
    var int head = 0,  var int count = 0
    var float sum = 0.0, var float sumSq = 0.0
    float oldest = array.get(buffer, head)
    if not na(oldest)
        sum -= oldest
        sumSq -= oldest * oldest
        count -= 1
    float val = nz(src)
    sum += val
    sumSq += val * val
    count += 1
    array.set(buffer, head, val)
    head := (head + 1) % p
    count > 1 ? math.sqrt(math.max(0.0, (sumSq / count) - math.pow(sum / count, 2))) : 0.0

correlation(series float src1, series float src2, simple int len) =>
    if len <= 0
        runtime.error("Period must be greater than 0")
    var int p = math.max(1, len)
    var array<float> buffer1 = array.new_float(p, na)
    var array<float> buffer2 = array.new_float(p, na)
    var int head = 0, var int count = 0
    var float sum1 = 0.0, var float sum2 = 0.0
    var float sumSq1 = 0.0, var float sumSq2 = 0.0
    var float sumProd = 0.0
    float oldest1 = array.get(buffer1, head)
    float oldest2 = array.get(buffer2, head)
    if not na(oldest1) and not na(oldest2)
        sum1 -= oldest1, sum2 -= oldest2
        sumSq1 -= oldest1 * oldest1, sumSq2 -= oldest2 * oldest2
        sumProd -= oldest1 * oldest2
        count -= 1
    if not na(src1) and not na(src2)
        sum1 += src1, sum2 += src2
        sumSq1 += src1 * src1, sumSq2 += src2 * src2
        sumProd += src1 * src2
        count += 1
        array.set(buffer1, head, src1)
        array.set(buffer2, head, src2)
    else
        array.set(buffer1, head, na)
        array.set(buffer2, head, na)
    head := (head + 1) % p
    if count > 1
        mean1 = sum1 / count, mean2 = sum2 / count
        cov = (sumProd / count) - mean1 * mean2
        var1 = (sumSq1 / count) - mean1 * mean1
        var2 = (sumSq2 / count) - mean2 * mean2
        stddev1 = math.sqrt(math.max(0.0, var1))
        stddev2 = math.sqrt(math.max(0.0, var2))
        denominator = stddev1 * stddev2
        if denominator != 0
            cov / denominator
        else
            na
    else
        na

//@function Calculates the cointegration of two series using the Engle-Granger method.
//@param series_a series float The first series.
//@param series_b series float The second series.
//@param period int The lookback period for the regression and ADF test.
//@returns float The Augmented Dickey-Fuller test statistic for the residuals. A more negative value suggests stronger evidence of cointegration.
//@optimized for performance and dirty data
cointegration(series_a, series_b, period) =>
    // Validate parameters
    if period <= 1
        runtime.error("Period must be greater than 1")
    beta = correlation(series_a, series_b, period) * (stddev(series_a, period) / stddev(series_b, period))
    alpha = sma(series_a, period) - beta * sma(series_b, period)
    residuals = series_a - (alpha + beta * series_b)
    delta_residuals = residuals - nz(residuals[1])
    lagged_residuals = nz(residuals[1])
    gamma_numerator = sma(delta_residuals * lagged_residuals, period - 1) - sma(delta_residuals, period - 1) * sma(lagged_residuals, period - 1)
    gamma_denominator = sma(lagged_residuals * lagged_residuals, period - 1) - math.pow(sma(lagged_residuals, period - 1), 2)
    gamma = gamma_denominator == 0 ? na : gamma_numerator / gamma_denominator
    regression_error = delta_residuals - gamma * lagged_residuals
    se_gamma_sq = sma(regression_error * regression_error, period - 1) / gamma_denominator
    se_gamma = se_gamma_sq <= 0 or na(se_gamma_sq) ? na : math.sqrt(se_gamma_sq)
    adf_statistic = se_gamma == 0 or na(se_gamma) ? na : gamma / se_gamma
    adf_statistic

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

// Inputs
i_source1 = input.source(close, "Source 1")
i_source2_ticker = input.symbol("SPY", "Source 2 Ticker (e.g., SPY, AAPL)")
i_period = input.int(20, "Period", minval=2)

i_source2 = request.security(i_source2_ticker, timeframe.period, close, lookahead=barmerge.lookahead_off)

// Calculation
coint_stat = cointegration(i_source1, i_source2, i_period)

// Plot
plot(coint_stat, "Cointegration ADF Stat", color.yellow, color=color.yellow, linewidth=2)