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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
83 lines
3.6 KiB
Plaintext
83 lines
3.6 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("Jarque-Bera Test (JB)", "JB", overlay=false, precision=4)
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// Helper function to get a window of series data into an array
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_get_window_array(series float source, simple int length) =>
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float[] arr = array.new_float(length)
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for i = 0 to length - 1
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array.set(arr, i, source[length - 1 - i]) // Oldest to newest
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arr
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// Helper function to calculate the k-th central moment
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// m_k = sum((x_i - mean)^k) / n
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_central_moment(float[] arr, int moment_order, float mean_val) =>
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n = array.size(arr)
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if n == 0
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float(na)
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else
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sum_pow_diff = 0.0
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for i = 0 to n - 1
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sum_pow_diff += math.pow(array.get(arr, i) - mean_val, moment_order)
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sum_pow_diff / n
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//@function Calculates the Jarque-Bera statistic.
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//@param source series float The input series.
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//@param length simple int The lookback period (sample size). Min 10.
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//@returns series float The Jarque-Bera statistic. Higher values suggest deviation from normality.
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jb_stat(series float source, simple int length) => // Renamed function for clarity jb_stat -> jb
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if length < 10 // Need sufficient sample size
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float(na)
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else
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float[] window_arr = _get_window_array(source, length)
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float mean_val = array.avg(window_arr) // Pine Script built-in array average
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if na(mean_val)
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float(na)
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else
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// Calculate variance (2nd central moment)
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float m2 = _central_moment(window_arr, 2, mean_val)
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if na(m2) or m2 < 1e-10 // Avoid division by zero or near-zero std dev
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float(na) // Or 0 if data is truly constant, but JB is ill-defined
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else
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float stddev_val = math.sqrt(m2)
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// Calculate 3rd central moment for skewness
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float m3 = _central_moment(window_arr, 3, mean_val)
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float s = m3 / math.pow(stddev_val, 3) // Skewness
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// Calculate 4th central moment for kurtosis
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float m4 = _central_moment(window_arr, 4, mean_val)
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float k_raw = m4 / math.pow(stddev_val, 4) // Raw Kurtosis
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float ek = k_raw - 3.0 // Excess Kurtosis
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if na(s) or na(ek)
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float(na)
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else
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// Jarque-Bera statistic formula: JB = (n/6) * (S^2 + (EK^2)/4)
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float jb_value_calc = (length / 6.0) * (s * s + (ek * ek) / 4.0) // Renamed internal variable
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jb_value_calc
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// Inputs
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i_source = input.source(close, title="Source")
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i_length = input.int(20, title="Lookback Period (Sample Size)", minval=10, maxval=200, tooltip="Number of bars for calculation. Min 10. Max 200 due to array processing. Higher values provide more stable estimates but lag more.")
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// Calculation
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jb_value = jb_stat(i_source, i_length) // Call renamed function
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// Plot
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plot(jb_value, "Jarque-Bera Statistic", color=color.teal, linewidth=2)
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// Critical values for Chi-squared distribution with 2 degrees of freedom (approximate):
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// Significance Level | Critical Value
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// 10% (0.10) | 4.605
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// 5% (0.05) | 5.991
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// 1% (0.01) | 9.210
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// These lines can help interpret the JB statistic. If JB > critical value, reject null hypothesis of normality.
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hline(4.605, "Critical Value (10%)", color.gray, linestyle=hline.style_dotted, linewidth=1)
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hline(5.991, "Critical Value (5%)", color.orange, linestyle=hline.style_dashed, linewidth=1)
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hline(9.210, "Critical Value (1%)", color.red, linestyle=hline.style_solid, linewidth=1)
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