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fix(docs): correct .md documentation across errors, dynamics, filters, forecasts, momentum, numerics, oscillators, reversals, statistics, trends, volatility, volume
Deep review of all indicator categories verified .md headers against .cs WarmupPeriod, parameters, inputs, and outputs. Fixes include warmup corrections, parameter documentation, output type accuracy, and Pine Script alignment.
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Miha Kralj
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// Licensed under the Apache License, Version 2.0
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// © mihakralj
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//@version=6
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indicator("Autocorrelation Function (ACF)", "ACF", overlay=false)
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//@function Calculates autocorrelation at a specified lag using a circular buffer
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//@param src series float Input data series
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//@param len simple int Lookback period for calculation
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//@param lag simple int Lag order for autocorrelation (default 1)
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//@returns float Autocorrelation coefficient between -1 and 1
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//@optimized for performance using running sums and biased estimator (divide by n)
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acf(series float src, simple int len, simple int lag) =>
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if len <= 0
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runtime.error("Period must be greater than 0")
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if lag < 1
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runtime.error("Lag must be at least 1")
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if len <= lag + 1
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runtime.error("Period must be greater than lag + 1")
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var int p = math.max(1, len)
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var array<float> buffer = array.new_float(p, na)
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var int head = 0, var int count = 0
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float oldest = array.get(buffer, head)
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if not na(oldest)
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count -= 1
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if not na(src)
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array.set(buffer, head, src)
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count += 1
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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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if count <= lag
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na
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else
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// Calculate mean
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float sum = 0.0
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int validN = 0
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for i = 0 to p - 1
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float val = array.get(buffer, i)
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if not na(val)
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sum += val
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validN += 1
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if validN <= lag
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na
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else
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float mean = sum / validN
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// Calculate variance (population): Σ(x - mean)² / n
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float variance = 0.0
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for i = 0 to p - 1
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float val = array.get(buffer, i)
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if not na(val)
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float diff = val - mean
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variance += diff * diff
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variance /= validN
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if variance <= 0
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0.0
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else
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// Calculate autocovariance at lag k (biased: divide by n)
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// Need to iterate in temporal order through the circular buffer
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int startIdx = count < p ? 0 : head
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float autocovariance = 0.0
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for t = lag to count - 1
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int currentIdx = (startIdx + t) % p
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int laggedIdx = (startIdx + t - lag) % p
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float xt = array.get(buffer, currentIdx)
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float xtk = array.get(buffer, laggedIdx)
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if not na(xt) and not na(xtk)
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autocovariance += (xt - mean) * (xtk - mean)
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autocovariance /= validN
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// ACF = γ_k / γ_0, clamped to [-1, 1]
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float result = autocovariance / variance
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math.max(-1.0, math.min(1.0, 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(20, "Period", minval=3)
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i_lag = input.int(1, "Lag", minval=1)
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// Calculation
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acf_value = acf(i_source, i_period, i_lag)
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// Plot
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plot(acf_value, "ACF", color=color.yellow, linewidth=2)
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// Licensed under the Apache License, Version 2.0
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// © mihakralj
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//@version=6
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indicator("Partial Autocorrelation Function (PACF)", "PACF", overlay=false)
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//@function Calculates partial autocorrelation at a specified lag using Durbin-Levinson recursion
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//@param src series float Input data series
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//@param len simple int Lookback period for calculation
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//@param lag simple int Lag order for partial autocorrelation (default 1)
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//@returns float Partial autocorrelation coefficient between -1 and 1
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//@optimized using Durbin-Levinson recursion to remove shorter-lag effects
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pacf(series float src, simple int len, simple int lag) =>
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if len <= 0
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runtime.error("Period must be greater than 0")
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if lag < 1
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runtime.error("Lag must be at least 1")
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if len <= lag + 1
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runtime.error("Period must be greater than lag + 1")
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var int p = math.max(1, len)
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var array<float> buffer = array.new_float(p, na)
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var int head = 0, var int count = 0
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float oldest = array.get(buffer, head)
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if not na(oldest)
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count -= 1
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if not na(src)
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array.set(buffer, head, src)
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count += 1
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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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if count <= lag
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na
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else
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// Calculate mean
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float sum = 0.0
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int validN = 0
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for i = 0 to p - 1
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float val = array.get(buffer, i)
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if not na(val)
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sum += val
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validN += 1
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if validN <= lag
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na
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else
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float mean = sum / validN
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// Calculate variance (population): Σ(x - mean)² / n
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float variance = 0.0
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for i = 0 to p - 1
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float val = array.get(buffer, i)
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if not na(val)
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float diff = val - mean
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variance += diff * diff
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variance /= validN
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if variance <= 0
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0.0
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else
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// Calculate ACF for lags 0 to target lag
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int startIdx = count < p ? 0 : head
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array<float> acfValues = array.new_float(lag + 1, 0.0)
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array.set(acfValues, 0, 1.0)
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for k = 1 to lag
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float autocovariance = 0.0
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for t = k to count - 1
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int currentIdx = (startIdx + t) % p
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int laggedIdx = (startIdx + t - k) % p
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float xt = array.get(buffer, currentIdx)
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float xtk = array.get(buffer, laggedIdx)
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if not na(xt) and not na(xtk)
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autocovariance += (xt - mean) * (xtk - mean)
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autocovariance /= validN
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array.set(acfValues, k, autocovariance / variance)
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// Durbin-Levinson recursion
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float pacfResult = na
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if lag == 1
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// PACF at lag 1 equals ACF at lag 1
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pacfResult := array.get(acfValues, 1)
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else
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array<float> phi = array.new_float(lag + 1, 0.0)
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array<float> phiPrev = array.new_float(lag + 1, 0.0)
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// Initialize: φ_11 = r_1
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array.set(phi, 1, array.get(acfValues, 1))
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// Iterate for k = 2 to target lag
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for k = 2 to lag
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// Copy phi to phiPrev
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for j = 0 to lag
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array.set(phiPrev, j, array.get(phi, j))
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// numerator = r_k - Σ(φ_{k-1,j} * r_{k-j}) for j=1..k-1
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float numerator = array.get(acfValues, k)
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for j = 1 to k - 1
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numerator -= array.get(phiPrev, j) * array.get(acfValues, k - j)
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// denominator = 1 - Σ(φ_{k-1,j} * r_j) for j=1..k-1
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float denominator = 1.0
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for j = 1 to k - 1
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denominator -= array.get(phiPrev, j) * array.get(acfValues, j)
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if math.abs(denominator) < 1e-15
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pacfResult := 0.0
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break
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// φ_kk = numerator / denominator
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array.set(phi, k, numerator / denominator)
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// Update: φ_kj = φ_{k-1,j} - φ_kk * φ_{k-1,k-j}
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for j = 1 to k - 1
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array.set(phi, j, array.get(phiPrev, j) - array.get(phi, k) * array.get(phiPrev, k - j))
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if na(pacfResult)
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pacfResult := array.get(phi, lag)
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// Clamp to [-1, 1]
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math.max(-1.0, math.min(1.0, pacfResult))
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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(20, "Period", minval=3)
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i_lag = input.int(1, "Lag", minval=1)
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// Calculation
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pacf_value = pacf(i_source, i_period, i_lag)
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// Plot
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plot(pacf_value, "PACF", color=color.yellow, linewidth=2)
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