Exponential Nadaraya Watson kernel regression [Jamallo]

17 مارس

(2025)

Intro

Nadaraya-Watson (N-W) kernel regression is a non-parametric smoothing technique that estimates the underlying trend of a price series without assuming any fixed model shape (like a straight line or curve). Unlike a simple moving average which weights bars equally, or an EMA which applies a fixed exponential decay, N-W regression derives its curve by computing a weighted average of all prices within a lookback window — where the weights are determined by a kernel function.

The most common kernel used is the Gaussian kernel, which assigns weights in a bell-curve shape — prices closer to the center of the window receive higher weight, prices at the edges receive lower weight. Most N-W implementations use a pure symmetric Gaussian kernel, meaning every bar within the lookback window is weighted purely by its distance from the center, with no preference for recency.

This indicator uses a hybrid Exponential Nadaraya-Watson (ENW) kernel that combines two weighting forces simultaneously:

• Gaussian spatial weight — bell-curve weighting centered on the window, same as standard N-W
• Exponential time-decay weight — progressively heavier weighting on recent bars, similar to how an EMA behaves

Both weights are multiplied together for each bar, meaning a price bar must be both spatially central and recent to receive maximum influence. In practice this shifts the effective weight peak toward the recent end of the window, making the K Line more responsive to current price action than standard N-W.

Breakdown

K Line — ENW Kernel Regression
The central baseline of the indicator. A smooth adaptive curve derived from the hybrid ENW kernel applied to closing prices. Bandwidth is controlled via the Kernel Length and Alpha inputs — higher alpha increases the recency bias, lower alpha brings behavior closer to standard N-W.

Volatility Bands (Inner & Outer)
Rather than using ATR or standard deviation for band width, this indicator measures the absolute deviation of price from the K Line and smooths that deviation through the same ENW kernel. This means bands are fully adaptive — they expand and contract organically based on how far price has been straying from the regression curve, not a fixed statistical formula. Inner and outer bands are independently scaled via deviation multipliers.

A Line — Vervoort ATR Stop
A trailing stop built on the HLC4 price source with an ATR-based loss distance. Flips direction on a close beyond the stop level. Serves as the primary trend bias line — when above the K Line the fill turns bullish, when below it turns bearish. Cross signals (triangles) are plotted whenever the A Line crosses the K Line, marking potential trend shifts.

Signal Line — Vervoort ATR Stop (Secondary)
A second independent Vervoort trailing stop running on its own ATR period and multiplier settings. Typically configured looser than the A Line — wider multiplier, longer or equal period — so it acts as a slower confirmation layer. Useful for filtering noise on the A Line crosses: an A Line cross that also aligns with the Signal Line's bias carries more weight than one that doesn't.
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Nadaraya-Watson kernel regression concept — E. Nadaraya (1964), G.S. Watson (1964)
Vervoort ATR Stop — Sylvain Vervoort

21 مارس

ملاحظات الأخبار

- tooltips, minor code sanitizing.