NW - Nadaraya-Watson Kernel Regression

// Licensed under the Apache License, Version 2.0
// © mihakralj

//@version=6
indicator("NW - Nadaraya-Watson Kernel Regression", "NW", overlay=true)

// ── Functions ──────────────────────────────────────────────────────────
// @function Calculates the Nadaraya-Watson kernel regression estimator
//   (Nadaraya 1964, Watson 1964) with Gaussian kernel.
//   Non-repainting endpoint estimation (backward-looking only).
//   For each bar t, computes the weighted average:
//     nw(t) = Σ_{i=0}^{N-1} w_i × src[i] / Σ_{i=0}^{N-1} w_i
//   where w_i = K(i/h) and K(u) = exp(-u²/2) is the Gaussian kernel.
//   The bandwidth h controls the effective smoothing radius:
//     small h → tight kernel → tracks price closely (low bias, high variance)
//     large h → wide kernel → heavy smoothing (high bias, low variance)
//   The period limits the lookback window; weights beyond ~3h are negligible.
//   Mathematically equivalent to a normalized Gaussian-weighted FIR filter
//   where the kernel width is parameterized by h rather than period.
// @param source Series to smooth
// @param period Lookback window (must be > 0)
// @param bandwidth Gaussian kernel bandwidth h (must be > 0)
// @returns NW kernel regression estimate
nw(series float source, simple int period, simple float bandwidth) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    if bandwidth <= 0
        runtime.error("Bandwidth must be greater than 0")

    float src = nz(source)
    int bars = math.min(bar_index + 1, period)

    // Nadaraya-Watson: weighted average with Gaussian kernel
    float num = 0.0
    float den = 0.0
    float h2x2 = 2.0 * bandwidth * bandwidth

    for i = 0 to bars - 1
        float dist = float(i)
        float w = math.exp(-(dist * dist) / h2x2)
        float val = nz(source[i])
        num += w * val
        den += w

    float result = den > 0.0 ? num / den : src
    result

// ── Inputs ─────────────────────────────────────────────────────────────
int    i_period    = input.int(64, "Period", minval=1)
float  i_bandwidth = input.float(8.0, "Bandwidth (h)", minval=0.1, step=0.5)
float i_source    = input.source(close, "Source")

// ── Calculation ────────────────────────────────────────────────────────
float value = nw(i_source, i_period, i_bandwidth)

// ── Plot ───────────────────────────────────────────────────────────────
plot(value, "NW", color.yellow, 2)