// PTA: Ehlers Precision Trend Analysis
// Category: Dynamics
// Based on: John F. Ehlers, "Precision Trend Analysis," TASC September 2024
//
// Dual highpass filter bandpass approach for near-zero-lag trend extraction.
// Trend = HP(longPeriod) - HP(shortPeriod)
// where HP is a 2-pole Butterworth highpass filter.
// Preserves cyclic components between shortPeriod and longPeriod.
// Output: zero-centered, positive = uptrend, negative = downtrend.

//@version=6
indicator("PTA - Ehlers Precision Trend Analysis", shorttitle="PTA", overlay=false)

// ── Inputs ──────────────────────────────────────────────────────
int longPeriod  = input.int(250, "Long Period",  minval=3)
int shortPeriod = input.int(40,  "Short Period", minval=2)

// ── Highpass Filter Function ────────────────────────────────────
highpass(float src, float period) =>
    float a1 = math.exp(-1.414 * math.pi / period)
    float b1 = 2.0 * a1 * math.cos(1.414 * math.pi / period)
    float c2 = b1
    float c3 = -a1 * a1
    float c1 = (1.0 + c2 - c3) * 0.25
    float hp = 0.0
    if bar_index >= 2
        hp := c1 * (src - 2.0 * src[1] + src[2]) + c2 * nz(hp[1]) + c3 * nz(hp[2])
    hp

// ── Calculations ────────────────────────────────────────────────
float hp1   = highpass(close, longPeriod)
float hp2   = highpass(close, shortPeriod)
float trend = hp1 - hp2

// ── Plots ───────────────────────────────────────────────────────
plot(trend, "PTA", color.red, 2)
hline(0, "Zero", color.gray, hline.style_dotted)