// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Third Derivative / Jerk (JERK)", "JERK", overlay=false, precision=8)

//@function Calculates the third finite difference (jerk): Jerk = V[t] - 3*V[t-1] + 3*V[t-2] - V[t-3]
//@param src Source series
//@returns Third difference. Returns 0.0 until 4 bars are available.
//@optimized Uses direct history access and binomial coefficients [1,-3,3,-1].
jerk(series float src) =>
    float v0 = src
    float v1 = src[1]
    float v2 = src[2]
    float v3 = src[3]
    if na(v1) or na(v2) or na(v3)
        0.0
    else
        v0 - 3.0 * v1 + 3.0 * v2 - v3

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

// Inputs
i_source = input.source(close, "Source")

// Calculation
j = jerk(i_source)

// Plot
plot(j, "Jerk", color=color.yellow, linewidth=2)