mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-07-27 17:27:43 +00:00
Miha Kralj
81 lines
3.7 KiB
Plaintext
81 lines
3.7 KiB
Plaintext
// Licensed under the Apache License, Version 2.0
|
|
// © mihakralj
|
|
//@version=6
|
|
indicator("Henderson Moving Average (HEND)", "HEND", overlay=true)
|
|
|
|
//@function Computes Henderson Moving Average — a symmetric FIR filter that preserves
|
|
// cubic polynomial trends without distortion, from the X-11 seasonal adjustment
|
|
// framework. Weights are derived from the closed-form Henderson formula and
|
|
// can be negative at the edges (bandpass-like property).
|
|
//@param source Series to smooth
|
|
//@param period Lookback window (must be odd >= 5)
|
|
//@returns Henderson-weighted moving average
|
|
//@reference Henderson, R. (1916). "Note on Graduation by Adjusted Average."
|
|
// Transactions of the Actuarial Society of America, 17, 43-48.
|
|
//@reference Hyndman, R.J. (2011). "Moving Averages" (International Encyclopedia of
|
|
// Statistical Science). Springer.
|
|
//@optimized O(period) per bar for convolution; weights precomputed once
|
|
hend(series float source, simple int period) =>
|
|
if period < 5
|
|
runtime.error("Period must be at least 5 for Henderson filter")
|
|
if period % 2 == 0
|
|
runtime.error("Period must be odd for Henderson filter")
|
|
|
|
float price = nz(source)
|
|
|
|
// --- Circular buffer for rolling window ---
|
|
var array<float> buffer = array.new_float(period, na)
|
|
var int head = 0
|
|
array.set(buffer, head, price)
|
|
head := (head + 1) % period
|
|
|
|
// --- Precompute Henderson weights once ---
|
|
// Formula: w(k) = 315 * [(n-1)^2 - k^2] * [n^2 - k^2] * [(n+1)^2 - k^2]
|
|
// * [3*n^2 - 16 - 11*k^2]
|
|
// / {8 * n * (n^2-1) * (4*n^2 - 1) * (4*n^2 - 9) * (4*n^2 - 25)}
|
|
// where n = (period + 3) / 2, k ranges from -(period-1)/2 to (period-1)/2
|
|
var array<float> weights = array.new_float(0)
|
|
if barstate.isfirst
|
|
int half = (period - 1) / 2
|
|
float n = (period + 3) / 2.0
|
|
float n2 = n * n
|
|
float nm1_2 = (n - 1) * (n - 1)
|
|
float np1_2 = (n + 1) * (n + 1)
|
|
float denom = 8.0 * n * (n2 - 1) * (4 * n2 - 1) * (4 * n2 - 9) * (4 * n2 - 25)
|
|
|
|
float wsum = 0.0
|
|
for k = -half to half
|
|
float k2 = float(k * k)
|
|
float w = 315.0 * (nm1_2 - k2) * (n2 - k2) * (np1_2 - k2) * (3 * n2 - 16 - 11 * k2) / denom
|
|
array.push(weights, w)
|
|
wsum += w
|
|
|
|
// Normalize weights to sum exactly 1.0 (handles floating-point drift)
|
|
if wsum != 0
|
|
for j = 0 to period - 1
|
|
array.set(weights, j, array.get(weights, j) / wsum)
|
|
|
|
int count = math.min(bar_index + 1, period)
|
|
if count < period
|
|
price
|
|
else
|
|
// --- Apply Henderson convolution via circular buffer ---
|
|
// Buffer position: head points to next-write = oldest entry
|
|
// Weight[0] corresponds to oldest bar, Weight[period-1] to newest
|
|
float result = 0.0
|
|
for j = 0 to period - 1
|
|
int idx = (head + j) % period
|
|
float val = nz(array.get(buffer, idx))
|
|
result += val * array.get(weights, j)
|
|
result
|
|
|
|
// ── Inputs ──────────────────────────────────────────────────────────────
|
|
src = input.source(close, "Source")
|
|
per = input.int(7, "Period", minval=5, step=2, tooltip="Must be odd, >= 5")
|
|
|
|
// Enforce odd period at input level
|
|
period_adj = per % 2 == 0 ? per + 1 : per
|
|
|
|
// ── Plot ────────────────────────────────────────────────────────────────
|
|
plot(hend(src, period_adj), "HEND", color.new(color.yellow, 0), 2)
|