// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Linear Trend Moving Average (LTMA)", "LTMA", overlay=true)

//@function Calculates LTMA using dual cascaded EMAs with linear trend extrapolation
//@param source Series to smooth
//@param period Lookback period (determines alpha = 2/(period+1))
//@returns LTMA value: lag-corrected EMA (equivalent to DEMA = 2·EMA1 − EMA2)
//@description Removes the EMA lag by estimating the per-bar slope from the spread
//  between two cascaded EMAs and projecting forward by exactly one lag interval.
//  EMA1 lags by τ = (1−α)/α bars; EMA1−EMA2 ≈ slope·τ; result = EMA1 + (EMA1−EMA2).
//  Initializing both EMAs to source on bar 1 gives zero warmup bias with no compensator needed.
ltma(series float source, simple int period) =>
    float alpha = 2.0 / (period + 1)
    float beta  = 1.0 - alpha

    var float ema1 = na
    var float ema2 = na

    float src = nz(source)

    if na(ema1)
        ema1 := src
        ema2 := src
    else
        ema1 := alpha * src + beta * ema1
        ema2 := alpha * ema1 + beta * ema2

    // slope = EMA1 − EMA2 ≈ slope_per_bar × lag
    // result = EMA1 + slope × 1.0  →  2·EMA1 − EMA2
    ema1 + (ema1 - ema2)

// ---------- Main loop ----------

i_period = input.int(14, "Period", minval=1)
i_source = input.source(close, "Source")

ltma_value = ltma(i_source, period=i_period)

plot(ltma_value, "LTMA", color=color.yellow, linewidth=2)