One-Sample t-Test (ZTEST)

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("One-Sample t-Test (ZTEST)", "t-TEST", overlay=false)

//@function Calculates the t-statistic for a one-sample hypothesis test
//@param source Source series to test (use returns for meaningful results)
//@param period Lookback period for calculating sample mean and standard deviation
//@param mu0 Hypothesized population mean to test against
//@returns t-statistic (positive values indicate sample mean > mu0, negative indicate sample mean < mu0)
//@optimized Uses circular buffer with running sums for O(1) complexity, Bessel correction for sample variance
ztest(series float source, simple int period, simple float mu0) =>
    if period <= 1
        runtime.error("Period must be greater than 1")
    
    int p = period
    var array<float> buffer = array.new_float(0)
    var int head = 0
    var int n = 0
    var float sum = 0.0
    var float sumSq = 0.0
    
    if array.size(buffer) != p
        buffer := array.new_float(p, na)
        head := 0
        n := 0
        sum := 0.0
        sumSq := 0.0
    
    float oldest = array.get(buffer, head)
    if not na(oldest)
        sum -= oldest
        sumSq -= oldest * oldest
        n -= 1
    
    if not na(source)
        sum += source
        sumSq += source * source
        n += 1
        array.set(buffer, head, source)
    else
        array.set(buffer, head, na)
    
    head := (head + 1) % p
    
    float result = na
    if n >= 2
        float nf = float(n)
        float mean = sum / nf
        float variance = math.max(0.0, (sumSq / nf) - (mean * mean)) * (nf / (nf - 1.0))
        float stddev = math.sqrt(variance)
        float standard_error = stddev / math.sqrt(nf)
        
        if standard_error > 1e-10
            result := (mean - mu0) / standard_error
    
    result

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

// Inputs
i_source = input.source(close, "Source")
i_period = input.int(30, "Period", minval=2, tooltip="Minimum 30 recommended for z-critical approximation")
i_mu0 = input.float(0.0, "Hypothesized Mean (μ₀)", step=0.01, tooltip="Use 0 when testing returns")

// Calculation
t_stat = ztest(i_source, i_period, i_mu0)

// Plot
plot(t_stat, "t-statistic", color=color.yellow, linewidth=2)
hline(0, "Zero Line", color=color.gray, linestyle=hline.style_dotted)
hline(2.04, "95% ~t(30)", color=color.new(color.green, 70), linestyle=hline.style_dashed)
hline(-2.04, "95% ~t(30)", color=color.new(color.green, 70), linestyle=hline.style_dashed)
hline(2.75, "99% ~t(30)", color=color.new(color.red, 70), linestyle=hline.style_dashed)
hline(-2.75, "99% ~t(30)", color=color.new(color.red, 70), linestyle=hline.style_dashed)