Iterative Locally Periodic EnvelopeThe Iterative Locally Periodic Envelope is a phase-conditioned kernel estimator with temporal locality and endogenous dispersion modeling, implemented as a Nadaraya–Watson estimator under a locally periodic kernel.
The locally periodic kernel defines similarity through cyclical phase alignment modulated by temporal proximity. Observations contribute to the estimator based on both their position within a repeating cycle structure and their recency, emphasizing structural recurrence with sensitivity to local regime conditions.
The indicator computes a latent equilibrium using a kernel-weighted mean and a dispersion measure using kernel-weighted variance under the same weighting structure. The resulting envelope reflects cycle-consistent deviation with temporal locality, rather than a conventional volatility band. All values are computed exclusively on closed historical bars using a bounded lookback window to ensure non-repainting behavior.
This indicator belongs to a broader class of iterative kernel-based envelopes that includes Gaussian, Rational Quadratic, and Periodic variants. All share a common Nadaraya–Watson estimation framework, differentiated by their kernel.
TRADING USES
The Iterative Locally Periodic Envelope is best interpreted as a cycle-aware structural estimator with adaptive temporal sensitivity, rather than a volatility-based band. The temporal locality component allows the estimator to adapt more readily to emerging regime shifts than the pure periodic variant.
Equilibrium Tracking
The latent equilibrium represents the phase-conditioned central tendency of price under locally periodic similarity weighting. Oscillations around this level reflect movement within a repeating structural cycle, with more recent phase-aligned observations contributing more strongly than temporally distant ones.
Cycle Regime Structure
The envelope emphasizes repeating structural behavior through phase recurrence weighting, modulated by temporal decay. Changes in symmetry, amplitude, or persistence of oscillation around the latent equilibrium may indicate transitions between cyclical regimes.
Mean Reversion Within Cycles
When a stable periodic structure is present, deviations from the latent equilibrium may revert toward phase-consistent levels. Mean-reversion behavior is conditioned on both cycle structure and temporal proximity.
Structural Extremes
Extreme deviations relative to the envelope correspond to phase-inconsistent states where cyclical structure becomes stretched or destabilized. Because the kernel incorporates temporal decay, these conditions are identified with greater sensitivity to recent price behavior.
State Estimation
The system defines a latent equilibrium as the inferred central cyclical state under joint phase and temporal weighting, with dispersion derived from kernel-weighted variance under identical constraints. This produces a structurally consistent representation of the market state that is sensitive to both cyclical position and local regime conditions.
LOCALLY PERIODIC ENVELOPE CONSTRUCTION
The envelope is constructed using kernel-weighted variance under the same locally periodic similarity measure used to estimate the latent equilibrium. The latent equilibrium defines the central state estimate and kernel-weighted variance defines dispersion under identical weighting, producing an endogenously determined envelope. The band width is fixed at ±1 kernel standard deviation with no multiplier, ensuring dispersion remains an intrinsic property of the locally periodic similarity structure rather than an externally imposed scaling parameter.
THEORY
The locally periodic kernel defines similarity in terms of cyclical phase recurrence modulated by temporal proximity. Observations contribute to the estimator based on alignment within a repeating cycle structure, with influence attenuated by temporal distance from the estimation point.
The estimator is formulated as a Nadaraya–Watson kernel regression under a locally periodic kernel, where weights are defined as:
k(i) = exp( -2 · sin²(πi / p) / L² ) · exp( -i² / 2L² )
Where:
p = period (cycle length)
L = lookback window (shared bandwidth parameter; effective smoothing scales with L²)
In this MacKay consistent formulation, the lookback window acts as a unified bandwidth parameter governing periodic phase selectivity and the Radial Basis Function (RBF) temporal decay envelope. The two components are coupled through L, producing a kernel that simultaneously emphasizes phase-aligned and temporally proximate observations.
As L increases, both the periodic and RBF components broaden, producing stronger smoothing across phase and time. As L decreases, phase selectivity and temporal locality both increase, making the estimator more sensitive to recent cycle-consistent observations.
This induces a similarity structure in which influence concentrates at phase-aligned intervals within a temporally bounded neighborhood. The resulting estimator defines a latent equilibrium governed by phase alignment and temporal proximity that can be interpreted as a locally stationary periodic extension of kernel regression on a circular phase manifold.
The key distinction from the pure periodic kernel is that phase-aligned observations at distant lags are progressively suppressed by the RBF decay term, allowing the estimator to adapt to structural drift while preserving cycle-aware weighting. During stable cyclical regimes the two estimators converge; during structural transitions the locally periodic variant adapts faster by downweighting older phase information.
CALIBRATION
As established in Gaussian Processes for Machine Learning (Rasmussen & Williams, 2006), the period should reflect the recurrence interval of the dominant cycle in the data, while the bandwidth parameter L controls how quickly similarity decays away from perfect phase alignment. For daily charts, common cycle anchors include the trading week (~5 bars), trading month (~21 bars), trading quarter (~63 bars), and trading year (~252 bars).
Length (Lookback / Bandwidth)
Controls structural depth of the estimator and acts as the unified bandwidth parameter for the periodic and RBF components; as L governs phase selectivity and temporal decay simultaneously, its effect is stronger than in the pure periodic variant. The default of 100 reflects the locally periodic kernel's temporal decay component; at longer lengths the RBF term weakens and behavior converges toward the pure periodic estimator.
- 50–100: high responsiveness, strong temporal locality, short-cycle sensitivity
- 150–250: balanced regime stability with moderate temporal decay
- 300+: broad structural smoothing, weak temporal decay, behavior converges toward pure periodic envelopes
Period (Cycle Length)
Defines the recurrence interval of the kernel and governs phase alignment and cyclical structure. Shorter periods increase phase resolution and cycle sensitivity, while longer periods emphasize broader structural recurrence. The period should reflect the dominant cycle present in the data, aligned with the anchor scales defined above.
Start At Bar
Offsets the kernel window backward from the most recent bars and excludes newer observations from the estimator. This ensures all calculations are based strictly on closed historical data and preserves non-repainting behavior.
MARKET USAGE
Stock, Forex, Crypto, Commodities, and Indices.
Performance is dependent on the presence of stable cyclical structure; in regimes lacking periodic coherence, the estimator converges toward a local smoother with reduced phase discrimination. Indicator
Iterative Periodic EnvelopeThe Iterative Periodic Envelope is a phase-conditioned kernel estimator with endogenous dispersion modeling, implemented as a Nadaraya–Watson estimator under a canonical periodic kernel.
The periodic kernel defines similarity through cyclical phase alignment rather than temporal proximity or multi-scale distance decay. Observations contribute to the estimator based on their position within a repeating cycle structure, emphasizing structural recurrence over linear time dependence.
The indicator computes a latent equilibrium using a kernel-weighted mean and a dispersion measure using kernel-weighted variance under the same weighting structure. The resulting envelope reflects cycle-consistent deviation, rather than a conventional volatility band. All values are computed exclusively on closed historical bars using a bounded lookback window, ensuring non-repainting behavior.
This indicator belongs to a broader class of iterative kernel-based envelopes that includes Gaussian and Rational Quadratic variants. All share a common Nadaraya–Watson estimation framework, differentiated by their kernel.
TRADING USES
The Iterative Periodic Envelope is best interpreted as a cycle-aware structural estimator rather than a volatility-based band.
Equilibrium Tracking
The latent equilibrium represents the phase-conditioned central tendency of price under periodic similarity weighting. Oscillations around this level reflect movement within a repeating structural cycle rather than directional drift.
Cycle Regime Structure
The envelope emphasizes repeating structural behavior through phase recurrence weighting. Changes in symmetry, amplitude, or persistence of oscillation around the latent equilibrium may indicate transitions between cyclical regimes.
Mean Reversion Within Cycles
When a stable periodic structure is present, deviations from the latent equilibrium may revert toward phase-consistent levels. This supports mean-reversion behavior that is conditioned on cycle structure rather than purely statistical dispersion.
Structural Extremes
Extreme deviations relative to the envelope correspond to phase-inconsistent states where cyclical structure becomes stretched or destabilized. These conditions often precede transitions such as cycle inversion, expansion, or compression.
State Estimation
The system defines a latent equilibrium as the inferred central cyclical state, with dispersion derived from kernel-weighted variance under identical periodic similarity constraints. This produces a structurally consistent representation of market state.
PERIODIC ENVELOPE CONSTRUCTION
The envelope is constructed using kernel-weighted variance under the same periodic similarity measure used to estimate the latent equilibrium. The latent equilibrium defines the central state estimate and kernel-weighted variance defines dispersion under identical weighting, producing an endogenously determined envelope. The band width is fixed at ±1 kernel standard deviation with no multiplier, ensuring dispersion remains an intrinsic property of the periodic similarity structure rather than an externally imposed scaling parameter.
THEORY
The periodic kernel defines similarity in terms of cyclical phase recurrence rather than linear temporal distance. Observations contribute to the estimator based on alignment within a repeating cycle structure.
The estimator is formulated as a Nadaraya–Watson kernel regression under a canonical periodic kernel, where weights are defined as:
k(i) = exp( -2 · sin²(πi / p) / L² )
Where:
p = period (cycle length)
L = lookback window (bandwidth parameter; effective smoothing scales with L²)
In this MacKay consistent formulation, the lookback window acts as a bandwidth control parameter, governing phase selectivity and structural smoothing. As L increases, the kernel becomes broader, producing stronger smoothing and reduced phase sensitivity. As L decreases, phase selectivity increases and the estimator becomes more locally sensitive to cyclical alignment.
This induces a cyclical similarity structure in which influence concentrates at recurring phase intervals. The resulting estimator defines a latent equilibrium governed by phase alignment rather than temporal proximity. This formulation can be interpreted as a periodic extension of kernel regression on a circular phase manifold.
CALIBRATION
Length (Lookback / Bandwidth)
Controls structural depth of the estimator and acts as the primary kernel bandwidth parameter.
- 50–100: high responsiveness, short-cycle sensitivity
- 150–250: balanced regime stability
- 300+: strong structural smoothing, reduced sensitivity to phase noise
Period (Cycle Length)
Defines the recurrence interval of the kernel and governs phase alignment and cyclical structure. Commonly aligns with dominant market rhythms such as intraday or macro-cycle structure.
- Lower values: faster cycle sensitivity
- Higher values: slower, broader structural cycles
Start At Bar
Offsets the kernel window backward from the most recent bars and excludes newer observations from the estimator. This ensures all calculations are based strictly on closed historical data and preserves non-repainting behavior.
MARKET USAGE
Stock, Forex, Crypto, Commodities, and Indices.
Performance is dependent on the presence of stable cyclical structure; in regimes lacking periodic coherence, the estimator converges toward a smoother, low-information state. Indicator
Meridian Lens PRO🟦 Meridian Lens PRO is a multi-kernel trend indicator built on the KernelLens Nadaraya–Watson regression library (a_jabbaroff/KernelLens/1). Three independently configurable kernel lines — Fast, Medium, and Slow — cover the full reactivity spectrum from scalping to position trading, each accepting any of the eight kernel families and three filter modes exposed by the library. The visual layer applies volume-intensity-adaptive coloring, gradient-filled trailing bands, 3-layer neon glow signal arrows, and a theme-aware dashboard — all driven by a single theme selection from ten optical-brand palettes.
🟦 HOW IT WORKS
Meridian Lens PRO calls the KernelLens library's unified dispatcher (`kl.estimate`) three times per bar — once for each kernel line:
```
Fast = kl.estimate(type, src, bw=8, α, period, phase, filter)
Medium = kl.estimate(type, src, bw=16, α, period, phase, filter)
Slow = kl.estimate(type, src, bw=32, α, period, phase, filter)
```
Each line independently selects its kernel family (Rational Quadratic, Gaussian, Periodic, Locally Periodic, Epanechnikov, Tricube, Triangular, Cosine), its filter mode (No Filter / Smooth / Zero Lag), its bandwidth, shape α, period, phase, and line width. The library handles all weighted-sum computation, loop-depth selection, NA-safe iteration, and input validation internally.
The Medium line is the primary trend reference — it drives the trailing bands, the main signal arrows, the dashboard trend cell, and the direction variable that colors every visual component. The Fast line provides early-warning reactivity for short-term entry timing. The Slow line anchors the macro trend for crossover logic and confluence scoring.
🟦 KERNEL LIBRARY INTEGRATION
Meridian Lens imports the published KernelLens library and uses the following exports:
| Library Export | Used For |
|---|---|
| `kl.estimate()` | Unified dispatcher — routes to the correct kernel based on user's dropdown selection |
| `kl.trendState()` | Returns +1 / −1 / 0 for each kernel's slope — drives dashboard arrows and signal triggers |
| `kl.crossSignal()` | Detects Fast × Slow crossovers — drives the Cross row in the dashboard and crossover alerts |
The indicator does not reimplement any kernel math — all regression computation is delegated to the library, ensuring that every bug fix or optimization in the library automatically propagates to this indicator.
🟦 THREE KERNEL LINES
**Fast Kernel** — The most reactive line. Default bandwidth 8, No Filter. Designed for scalping and short-term entry timing. Flips direction frequently on noisy charts — its signal markers are OFF by default to avoid visual clutter.
**Medium Kernel** — The primary trend reference. Default bandwidth 16, Smooth filter. Drives the trailing bands, the main 3-layer glow signal arrows, the dashboard Trend cell, and the direction variable that colors every visual component. This is the indicator's core signal.
**Slow Kernel** — The macro trend anchor. Default bandwidth 32, Smooth filter. Provides structural support for crossover logic (Fast × Slow) and triple-line confluence scoring. Its signal markers are ON by default because Slow flips are rare and meaningful.
Each kernel group exposes: Show toggle, Kernel Type dropdown (8 families), Bandwidth, Shape α (RQ only), Period (Periodic / Locally Periodic only), Phase (non-repainting offset), Filter (None / Smooth / Zero Lag), and Line Width.
🟦 NON-REPAINTING BEHAVIOR
Meridian Lens inherits non-repainting behavior directly from the KernelLens library's `_phase` parameter. Each kernel line has its own Phase input (default: 2), which shifts the kernel center into the past by that many bars.
- Phase = 0 — live estimate, flickers on the current bar (real-time only; history is immutable)
- Phase = 1 — 1-bar lag, non-repainting once the bar is confirmed
- Phase = 2 — recommended balance between freshness and stability (default)
- Phase = 3+ — extra stability for swing and position trading
Historical repainting never occurs at any phase value. The library contains no `request.security` calls, no lookahead, and no array rotation that could leak future data. Every historical bar's plotted value is final once confirmed.
🟦 SIGNAL SYSTEM
The indicator produces three tiers of trend-flip signals, each visually distinct:
**Medium Signals (Primary)** — 3-layer neon glow arrows rendered when the Medium kernel's direction flips. The outer halo is large and 80% transparent, the middle layer is normal-sized and 50% transparent, and the core arrow is small and fully opaque — creating a luminous halo effect on dark charts. Controlled by the "Glow Effect" toggle.
**Slow Signals** — Minimal tiny arrows (40% transparent) that fire when the Slow kernel flips direction. ON by default — these mark rare, meaningful macro trend changes.
**Fast Signals** — Minimal tiny arrows (40% transparent) that fire when the Fast kernel flips direction. OFF by default — enable for early-warning entry timing on lower timeframes.
🟦 VISUAL PIPELINE
**Volume-Intensity Adaptive Color** — The Medium line's transparency responds to the current volume reading. High volume = bright line (volume-confirmed trend), low volume = dim line (low-conviction drift). Uses a 33-bar HMA-smoothed normalized volume metric. Disable for a fixed 50% transparency.
**Trailing Bands** — Gradient-filled bands on the bullish/bearish side of the Medium line. Band width is driven by the rolling 100-bar average candle body size multiplied by a configurable distance factor (default: 2.0×). Bull bands fill below the Medium line during uptrends, bear bands fill above during downtrends.
**Theme System** — Ten cohesive palettes drive every visual component:
| Theme | Bull | Bear |
|---|---|---|
| Prism | Forest green | Crimson red |
| Focus | Cyan steel | Deep orange |
| Solar | Warm amber | Indigo red |
| Frost | Sky blue | Soft lavender |
| Laser | Neon lime | Hot crimson |
| Aurora | Bright gold | Scarlet |
| Plasma | Electric aqua | Magenta |
| Bloom | Mint green | Hot pink |
| Eclipse | Deep navy | Dark crimson |
| Carbon | Near-black | Silver grey |
🟦 PRO DASHBOARD
A 2-column, 11-row theme-aware status panel that updates only on the last bar (zero historical overhead). Supports Dark and Light display modes with configurable position and text size.
| Row | Label | Content |
|---|---|---|
| Header | MERIDIAN LENS | DARK / LIGHT |
| Theme | Theme | Active palette name |
| Kernel | Kernel | Medium kernel type |
| Divider | KERNELS | — |
| Fast | Fast | ▲/▼ + price value (bull/bear colored) |
| Medium | Medium | ▲/▼ + price value (bull/bear colored) |
| Slow | Slow | ▲/▼ + price value (bull/bear colored) |
| Divider | SIGNALS | — |
| Trend | Trend | ▲ BULL / ▼ BEAR |
| Cross | Cross | ↑ UP / ↓ DOWN / — |
| Strength | Strength | ▰▰▰ TRIPLE / ▰▰▱ STRONG / ▰▱▱ WEAK / ▱▱▱ NEUTRAL |
**Confluence Strength** — Counts how many of the three kernels (Fast, Medium, Slow) have their trend aligned with the Medium's direction. Score 3 = TRIPLE BULL/BEAR, 2 = STRONG, 1 = WEAK, 0 = NEUTRAL.
🟦 ALERT CONDITIONS
Six opt-in alert conditions, each gated by its own toggle:
| Alert | Fires When |
|---|---|
| Bull Crossover | Fast line crosses above Slow line |
| Bear Crossover | Fast line crosses below Slow line |
| Trend Up | Medium kernel trend flips to rising |
| Trend Down | Medium kernel trend flips to falling |
| Triple Bullish | Fast > Medium > Slow AND Medium rising |
| Triple Bearish | Fast < Medium < Slow AND Medium falling |
All alerts use `alertcondition()` for maximum compatibility with PulseWire's alert system including webhooks.
🟦 RECOMMENDED PRESETS
| Style | Fast bw | Med bw | Slow bw | Phase | Med Filter | Chart |
|---|---|---|---|---|---|---|
| Scalper | 4–8 | 8–16 | 16–32 | 1 | No Filter | 1m–5m |
| Day Trader | 8–12 | 14–24 | 24–48 | 2 | Smooth | 15m–1h |
| Swing | 16–24 | 24–40 | 48–80 | 2 | Smooth | 4h–1D |
| Position | 24–48 | 40–80 | 80–200 | 3 | Smooth | 1D–1W |
🟦 COMPATIBILITY
- Pine Script v6
- All exchanges, all asset classes (crypto, forex, equities, commodities)
- All timeframes (1 minute through Monthly)
- No exchange-specific logic — fully deterministic
🟦 TECHNICAL NOTES
- **Library dependency** — `import a_jabbaroff/KernelLens/1` — all kernel regression math is delegated to the library
- **Plot budget** — 5 plots + 2 fills + 10 plotshapes = well under Pine's 64-plot limit
- **Table** — Single `var table` created once on `barstate.islast`, zero historical overhead
- **No persistent drawing objects** — no `box.new`, `label.new`, `line.new` — no garbage collection needed
- **Non-repainting** — inherits from the library's `_phase` parameter; no `request.security`, no lookahead
- **Volume-intensity** — uses HMA-smoothed normalized volume (33-bar window) for adaptive transparency
🟦 DISCLAIMER
Meridian Lens PRO is a technical analysis overlay indicator built on the KernelLens Nadaraya–Watson regression library. It is provided solely for educational and research purposes and does not constitute financial, investment, or trading advice.
Kernel regression is a local smoothing technique. It estimates the mean of a source series in the neighborhood of the current bar based on historical data, but it does not predict future prices, does not generate trading signals on its own, and does not guarantee the profitability of any strategy built on top of its output.
Past performance of any model does not guarantee future results. Markets contain systemic risks that cannot be eliminated by any amount of mathematical rigor. Responsibility for any trading decisions rests entirely with the user. Always apply sound capital management, conduct your own independent analysis, and never risk capital you are not prepared to lose.
The author assumes no liability for direct or indirect losses incurred through the use of Meridian Lens or the underlying KernelLens library.
Indicator
Iterative Rational Quadratic ChannelThe Iterative Rational Quadratic Channel is a kernel-based smoothing and state estimation framework that applies a Rational Quadratic kernel regression to price data, combined with a rolling standard deviation envelope to construct adaptive dynamic channel boundaries.
Unlike exponential kernel methods that prioritize recent data at the expense of historical context, the rational quadratic kernel introduces a heavy-tailed weighting structure that preserves multi-scale memory in price dynamics. This enables the channel to reflect not only short-term fluctuations, but also broader structural regime context.
The resulting channel is less reactive to micro-noise and more representative of persistent market structure, making it particularly effective for trend continuity analysis, regime modeling, and reducing sensitivity to false reversals.
Its primary utility is as a state estimation and regime-filtering tool for price behavior, rather than a pure high-frequency signal isolation tool.
TRADING USES
The Rational Quadratic Channel is best interpreted as a regime-aware structural filter rather than a purely reactive trading band.
Trend Continuity
The channel basis line (RQ smoothed price) provides a stable representation of underlying market direction. Sustained movement above or below the basis reflects trend persistence rather than short-lived fluctuations, making it useful for maintaining directional bias.
Regime Persistence
Due to the heavy-tailed memory of the rational quadratic kernel, historical price structure continues to influence current valuation. This produces smoother transitions between market phases and reduces sensitivity to short-term reversals, improving regime stability.
False Reversal Filtering
Compared to exponentially weighted kernels, the RQ channel reduces overreaction to transient volatility spikes. This helps filter out low-quality reversals driven by noise rather than structural change.
State Estimation
The channel functions as a continuous estimator of market state:
- The basis represents the inferred latent price state
- The envelope represents dynamic volatility dispersion around that state
This makes it well-suited for manual, semi-automated, and automated trading systems requiring a stable structural representation of price rather than raw responsiveness. Gradual shifts in the basis line and channel position can also serve as a framework for monitoring changes in trend direction and regime transitions over time.
Volatility & Risk Context
The rolling standard deviation envelope expands and contracts based on realized volatility, providing a contextual risk framework. Wider channels indicate increased uncertainty and dispersion, while tighter channels indicate compression and lower variance conditions.
THEORY
The rational quadratic kernel is a member of the scale-mixture family of Gaussian kernels and can be interpreted as a superposition of Gaussian processes operating at multiple length scales. This allows it to capture both local and global structure in time series data.
It is defined as:
k(i)=(1+i22αℓ2)−αk(i) = \left(1 + \frac{i^2}{2\alpha \ell^2}\right)^{-\alpha}k(i)=(1+2αℓ2i2)−α
Where:
---> α\alphaα controls tail heaviness (relativeWeight)
---> ℓ\ellℓ defines the characteristic scale (lookback)
Unlike Gaussian kernels, which enforce exponential decay and emphasize locality, the rational quadratic kernel follows a power-law decay. This allows older observations to retain influence over the estimator for longer periods, producing a smoothing effect that is inherently multi-scale and well-suited for modeling persistent structural behavior.
The rolling standard deviation complements this by measuring dispersion around the estimated state, forming a volatility-adaptive envelope. Rather than acting as a strict statistical confidence interval, it provides a dynamic representation of market expansion and contraction.
The iterative implementation processes data sequentially (bar-by-bar), ensuring computational efficiency and making the indicator suitable for real-time use without repainting.
CALIBRATION
Calibration determines the balance between responsiveness, structural memory, and regime stability.
Length (Lookback)
Lower (50–100): More responsive, increased sensitivity to short-term structure
Medium (150–250): Balanced for swing trading and intermediate regimes
Higher (300+): Strong regime persistence, reduced sensitivity to noise
Relative Weight (Tail Sensitivity)
Controls how quickly historical influence decays:
Lower values (≈ 0.5 – 1.0):
- Behavior approaches Gaussian
- More responsive to recent price action
- Faster detection of trend changes
- Slightly more sensitive to noise
Higher values (≈ 2.0+):
- Stronger heavy-tail behavior
- Increased influence of older price data
- Smoother output and stronger regime anchoring
- Improved false reversal filtering
Start At Bar (Lag / Structural Anchoring)
Controls how much recent price data is excluded from the kernel calculation:
Lower values (0–10):
- Uses most recent data
- Faster reaction to price changes
- More sensitive to short-term volatility
Moderate values (10–30):
- Balanced responsiveness and stability
- Reduces noise without excessive lag
- Suitable for most trading environments
Higher values (30+):
- Strong structural anchoring
- Significantly reduced sensitivity to recent fluctuations
- Enhanced regime persistence
- Slower response to turning points
This parameter effectively introduces a controlled lag, allowing users to tune the tradeoff between responsiveness and regime stability.
MARKET USAGE
Stock, Forex, Crypto, Commodities, and Indices. Indicator
Exponential Nadaraya Watson kernel regression [Jamallo](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
Indicator
EDUVEST Lorentzian ClassificationEDUVEST Lorentzian Classification - Machine Learning Signal Detection
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
█ ORIGINALITY
This indicator enhances the original Lorentzian Classification concept by jdehorty with EduVest's visual modifications and alert system integration. The core innovation is using Lorentzian distance instead of Euclidean distance for k-NN classification, providing more robust pattern recognition in financial markets.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
█ WHAT IT DOES
- Generates BUY/SELL signals using machine learning classification
- Displays kernel regression estimate for trend visualization
- Shows prediction values on each bar
- Provides trade statistics (Win Rate, W/L Ratio)
- Includes multiple filter options (Volatility, Regime, ADX, EMA, SMA)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
█ HOW IT WORKS
【Lorentzian Distance Calculation】
Unlike Euclidean distance, Lorentzian distance uses logarithmic transformation:
d = Σ log(1 + |xi - yi|)
This provides:
- Better handling of outliers
- More stable distance measurements
- Reduced sensitivity to extreme values
【Feature Engineering】
The classifier uses up to 5 configurable features:
- RSI (Relative Strength Index)
- WT (WaveTrend)
- CCI (Commodity Channel Index)
- ADX (Average Directional Index)
Each feature is normalized using the n_rsi, n_wt, n_cci, or n_adx functions.
【k-Nearest Neighbors Classification】
1. Calculate Lorentzian distance between current bar and historical bars
2. Find k nearest neighbors (default: 8)
3. Sum predictions from neighbors
4. Generate signal based on prediction sum (>0 = Long, <0 = Short)
【Kernel Regression】
Uses Rational Quadratic kernel for smooth trend estimation:
- Lookback Window: 8
- Relative Weighting: 8
- Regression Level: 25
【Filters】
- Volatility Filter: Filters signals during extreme volatility
- Regime Filter: Identifies market regime using threshold
- ADX Filter: Confirms trend strength
- EMA/SMA Filter: Trend direction confirmation
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█ HOW TO USE
【Recommended Settings】
- Timeframe: 15M, 1H, 4H, Daily
- Neighbors Count: 8 (default)
- Feature Count: 5 for comprehensive analysis
【Signal Interpretation】
- Green BUY label: Long entry signal
- Red SELL label: Short entry signal
- Bar colors: Green (bullish) / Red (bearish) prediction strength
【Trade Statistics Panel】
- Winrate: Historical win percentage
- Trades: Total (Wins|Losses)
- WL Ratio: Win/Loss ratio
- Early Signal Flips: Premature signal changes
【Filter Recommendations】
- Enable Volatility Filter for ranging markets
- Enable Regime Filter for trend confirmation
- Use EMA Filter (200) for higher timeframes
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Original Lorentzian Classification concept and MLExtensions library by jdehorty.
Enhanced with visual modifications and alert integration by EduVest.
License: Mozilla Public License 2.0 Indicator
Indicator
KernelFunctionsFiltersLibrary "KernelFunctionsFilters"
This library provides filters for non-repainting kernel functions for Nadaraya-Watson estimator implementations made by @jdehorty. Filters include a smoothing formula and zero lag formula. You can find examples in the code. For more information check out the original library KernelFunctions.
rationalQuadratic(_src, _lookback, _relativeWeight, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
_relativeWeight (simple float)
startAtBar (simple int)
_filter (simple string)
gaussian(_src, _lookback, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
startAtBar (simple int)
_filter (simple string)
periodic(_src, _lookback, _period, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
_period (simple int)
startAtBar (simple int)
_filter (simple string)
locallyPeriodic(_src, _lookback, _period, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
_period (simple int)
startAtBar (simple int)
_filter (simple string)
j(line1, line2)
Parameters:
line1 (float)
line2 (float) Library
Indicator
Nadaraya-Watson Smoothers [LuxAlgo]The following tool smoothes the price data using various methods derived from the Nadaraya-Watson estimator, a simple Kernel regression method. This method makes use of the Gaussian kernel as a weighting function.
Users have the option to use a non-repainting as well as a repainting method, see the USAGE section for more information.
🔶 USAGE
🔹 Non Repainting
When Repainting Smoothing is disabled the returned indicator acts similarly to a regular causal moving average. This result could be described as an "endpoint Nadaraya-Watson estimator".
Unlike a regular moving average whose degree of smoothness is commonly determined by the length of its calculation window, the degree of smoothness of the proposed indicator is determined by the bandwidth setting, with a higher value returning smoother results.
In the above chart, a bandwidth value of 50 is used. An increasing value of the smoother is indicative of an uptrend, while a decreasing value is indicative of a downtrend.
🔹 Repainting
Non-causal smoothing methods have found low support from technical analysts because they tend to repaint. Yet, they can provide powerful insights such as estimating underlying trends in the price as well as seeing how far prices deviate from them. They can also make drawing certain patterns easier and can help see underlying structures in the price more clearly.
Using higher bandwidth values allows for estimating longer-term trends in the price.
Triangular labels highlight points where the direction of the estimator change. This allows for the identification of tops and bottoms in the underlying trend which can be compared to the actual price tops and bottoms.
Note that multiple labels can appear in real time, highlighting real-time changes in the estimator's direction. The most recent label on a series of labels is the first to appear. This can eventually be useful for the real-time predictive application of the estimator. However, it is not a usage we particularly recommend.
🔶 DETAILS
The Nadaraya-Watson estimator can be described as a series of weighted averages using a specific normalized kernel as a weighting function. For each point of the estimator at time t , the peak of the kernel is located at time t , as such the highest weights are attributed to values neighboring the price located at time t .
A lower bandwidth value would contribute toward a more important weighting of the price at a precise point and would as such less smooth results. In the case where our bandwidth is so small that the resulting kernel is just an impulse, we would get the raw price back.
However, when the bandwidth is sufficiently large, prices would be weighted similarly, thus resulting in a result closer to the price mean.
It can be interesting to note that due to the nature of the estimator and its weighting procedure, real-time results would not deviate drastically for points in the estimator near the center of the calculation window.
🔶 SETTINGS
Bandwidth : controls the bandwidth of the Gaussian kernel, with higher values returning smoother results.
Src : Input source of the kernel regression.
Repainting Smoothing : Determine if the smoothing method should repaint or not. If disabled the "endpoint Nadaraya-Watson estimator" is returned. Indicator
