mirror of
https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
80 lines
3.0 KiB
Plaintext
80 lines
3.0 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("Ehlers Ultimate Strength Index (USI)", "USI", overlay = false)
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//@function Ehlers Ultimate Strength Index — a symmetric RSI replacement that uses
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// the UltimateSmoother filter instead of Wilder's exponential smoothing.
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// Output is bounded [-1, +1], with bullish > 0 and bearish < 0.
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// Pipeline: SU/SD extraction → SMA(4) → UltimateSmoother(period) → normalize.
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//@param source Series of close prices
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//@param period UltimateSmoother filter period (default 28)
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//@returns USI value bounded [-1, +1]
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//@reference Ehlers, J.F. (2024). "Ultimate Strength Index (USI)."
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// Technical Analysis of Stocks & Commodities, Nov 2024.
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//@optimized O(1) per bar — inline SMA(4) circular buffer + IIR filter
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usi(series float source, simple int period) =>
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if period < 1
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runtime.error("Period must be at least 1")
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float src = nz(source)
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float prevSrc = nz(source[1])
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// --- Strength Up / Strength Down ---
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float su = src > prevSrc ? src - prevSrc : 0.0
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float sd = prevSrc > src ? prevSrc - src : 0.0
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// --- Simple Moving Average of SU and SD over 4 bars ---
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float avgSU = math.avg(su, nz(su[1]), nz(su[2]), nz(su[3]))
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float avgSD = math.avg(sd, nz(sd[1]), nz(sd[2]), nz(sd[3]))
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// --- UltimateSmoother coefficients ---
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float a1 = math.exp(-1.414 * math.pi / period)
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float c2 = 2.0 * a1 * math.cos(1.414 * math.pi / period)
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float c3 = -a1 * a1
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float c1 = (1.0 + c2 - c3) / 4.0
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// --- UltimateSmoother of avgSU ---
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var float usu = 0.0
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if bar_index < 7
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usu := avgSU
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else
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usu := (1.0 - c1) * avgSU + (2.0 * c1 - c2) * nz(avgSU[1]) - (c1 + c3) * nz(avgSU[2]) + c2 * nz(usu[1]) + c3 * nz(usu[2])
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// --- UltimateSmoother of avgSD ---
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var float usd = 0.0
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if bar_index < 7
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usd := avgSD
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else
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usd := (1.0 - c1) * avgSD + (2.0 * c1 - c2) * nz(avgSD[1]) - (c1 + c3) * nz(avgSD[2]) + c2 * nz(usd[1]) + c3 * nz(usd[2])
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// --- USI normalization ---
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float denom = usu + usd
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float eps = 0.01
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var float usiVal = 0.0
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if denom > eps
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usiVal := (usu - usd) / denom
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usiVal
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// ——— Inputs ———
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int prd = input.int(28, "Period", minval = 1, tooltip = "UltimateSmoother filter period")
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string src = input.string("Close", "Source", options = ["Open","High","Low","Close","HL2","HLC3","HLCC4","OHLC4"])
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// ——— Source selector ———
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float price = switch src
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"Open" => open
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"High" => high
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"Low" => low
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"HL2" => hl2
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"HLC3" => hlc3
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"HLCC4" => (high + low + close + close) / 4.0
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"OHLC4" => ohlc4
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=> close
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// ——— Calculation & plot ———
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float val = usi(price, prd)
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hline(0, "Zero", color.gray, hline.style_dotted)
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hline(0.4, "+0.4", color.new(color.green, 60), hline.style_dashed)
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hline(-0.4, "-0.4", color.new(color.red, 60), hline.style_dashed)
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plot(val, "USI", val >= 0 ? color.teal : color.red, 2)
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