Adaptive Quadratic Kernel Envelope

This study draws a fair-value curve from a quadratic-weighted (Nadaraya-Watson) regression. Alpha sets how sharply weights decay inside the look-back window, so you trade lag against smoothness with one slider. Band half-width is ATRslow times a bounded fast/slow ATR ratio, giving an instant response to regime shifts without overshooting on spikes. Work in log space when an instrument grows exponentially, equal percentage moves then map to equal vertical steps. NearBase and FarBase define a progression of adaptive thresholds, useful for sizing exits or calibrating mean-reversion logic. Non-repaint mode keeps one-bar delay for clean back-tests, predictive mode shows the zero-lag curve for live decisions.

Key points
- Quadratic weights cut phase error versus Gaussian or SMA-based envelopes.
- Dual-ATR scaling updates width on the next bar, no residual lag.
- Log option preserves envelope symmetry across multi-decade data.
- Alpha provides direct control of curvature versus noise.
- Built-in alerts trigger on the first adaptive threshold, ready for automation.

Typical uses
Trend bias from the slope of the curve.
Entry timing when price pierces an inner threshold and momentum stalls.
Breakout confirmation when closes hold beyond outer thresholds while volatility expands.
Stops and targets anchored to chosen thresholds, automatically matching current noise.