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https://github.com/mihakralj/QuanTAlib.git
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61 lines
2.0 KiB
Plaintext
61 lines
2.0 KiB
Plaintext
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// The MIT License (MIT)
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// © mihakralj
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//@version=6
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indicator("Linear Trend Moving Average (LTMA)", "LTMA", overlay=true)
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//@function Calculates Linear Trend MA using dual EMA with linear extrapolation
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//@param source Series to smooth
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//@param period Lookback period (determines alpha = 2/(period+1))
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//@returns LTMA value: EMA-based linear trend projection from first bar
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//@description LTMA tracks both level and slope using two cascaded EMAs,
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// then extrapolates the linear trend forward. Unlike DEMA (which cancels
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// first-order lag via 2×EMA1 − EMA2), LTMA estimates the instantaneous
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// slope from the EMA difference and projects it forward by the full period:
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// slope = (EMA1 − EMA2) / (decay − 1)
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// LTMA = EMA1 + slope × period
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// where decay = (1 − alpha). This produces a predictive moving average
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// that follows linear trends with zero steady-state error.
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// Uses §2 exponential warmup compensator on both EMAs (e*=beta,
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// c=1/(1-e)) for valid output from bar 1.
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ltma(series float source, simple int period) =>
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if period <= 0
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runtime.error("Period must be greater than 0")
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float alpha = 2.0 / (period + 1)
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float beta = 1.0 - alpha
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var bool warmup = true
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var float e = 1.0
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var float ema1 = 0.0
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var float ema2 = 0.0
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var float result = source
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float src = nz(source)
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ema1 := alpha * (src - ema1) + ema1
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ema2 := alpha * (ema1 - ema2) + ema2
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if warmup
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e *= beta
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float c = 1.0 / (1.0 - e)
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float comp1 = c * ema1
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float comp2 = c * ema2
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float slope = comp1 - comp2
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result := comp1 + slope * period
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warmup := e > 1e-10
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else
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float slope = ema1 - ema2
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result := ema1 + slope * period
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result
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// ---------- Main loop ----------
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// Inputs
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i_period = input.int(14, "Period", minval=1)
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i_source = input.source(close, "Source")
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// Calculation
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ltma_value = ltma(i_source, period=i_period)
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// Plot
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plot(ltma_value, "LTMA", color=color.yellow, linewidth=2)
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