mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-07-28 01:37:43 +00:00
Miha Kralj
76 lines
2.6 KiB
Plaintext
76 lines
2.6 KiB
Plaintext
// Licensed under the Apache License, Version 2.0
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// © mihakralj
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//@version=6
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indicator("One-Sample t-Test (ZTEST)", "t-TEST", overlay=false)
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//@function Calculates the t-statistic for a one-sample hypothesis test
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//@param source Source series to test (use returns for meaningful results)
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//@param period Lookback period for calculating sample mean and standard deviation
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//@param mu0 Hypothesized population mean to test against
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//@returns t-statistic (positive values indicate sample mean > mu0, negative indicate sample mean < mu0)
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//@optimized Uses circular buffer with running sums for O(1) complexity, Bessel correction for sample variance
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ztest(series float source, simple int period, simple float mu0) =>
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if period <= 1
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runtime.error("Period must be greater than 1")
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int p = period
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var array<float> buffer = array.new_float(0)
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var int head = 0
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var int n = 0
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var float sum = 0.0
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var float sumSq = 0.0
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if array.size(buffer) != p
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buffer := array.new_float(p, na)
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head := 0
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n := 0
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sum := 0.0
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sumSq := 0.0
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float oldest = array.get(buffer, head)
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if not na(oldest)
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sum -= oldest
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sumSq -= oldest * oldest
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n -= 1
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if not na(source)
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sum += source
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sumSq += source * source
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n += 1
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array.set(buffer, head, source)
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else
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array.set(buffer, head, na)
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head := (head + 1) % p
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float result = na
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if n >= 2
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float nf = float(n)
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float mean = sum / nf
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float variance = math.max(0.0, (sumSq / nf) - (mean * mean)) * (nf / (nf - 1.0))
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float stddev = math.sqrt(variance)
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float standard_error = stddev / math.sqrt(nf)
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if standard_error > 1e-10
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result := (mean - mu0) / standard_error
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result
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// ---------- Main loop ----------
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// Inputs
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i_source = input.source(close, "Source")
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i_period = input.int(30, "Period", minval=2, tooltip="Minimum 30 recommended for z-critical approximation")
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i_mu0 = input.float(0.0, "Hypothesized Mean (μ₀)", step=0.01, tooltip="Use 0 when testing returns")
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// Calculation
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t_stat = ztest(i_source, i_period, i_mu0)
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// Plot
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plot(t_stat, "t-statistic", color=color.yellow, linewidth=2)
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hline(0, "Zero Line", color=color.gray, linestyle=hline.style_dotted)
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hline(2.04, "95% ~t(30)", color=color.new(color.green, 70), linestyle=hline.style_dashed)
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hline(-2.04, "95% ~t(30)", color=color.new(color.green, 70), linestyle=hline.style_dashed)
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hline(2.75, "99% ~t(30)", color=color.new(color.red, 70), linestyle=hline.style_dashed)
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hline(-2.75, "99% ~t(30)", color=color.new(color.red, 70), linestyle=hline.style_dashed)
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