Laguerre Filter Node

Polynomial Basis Smoothing Filter

FilterSmoothingAdvanced

Overview

Laguerre Filter applies orthogonal polynomial basis functions to smooth price data with minimal lag. Unlike moving averages that use equal weighting, Laguerre functions weight recent data heavily while exponentially reducing older data emphasis. Result: unprecedented smoothness with almost no lag. Trending data passes through clean, choppy data gets eliminated. Perfect preprocessing filter before applying oscillators or momentum indicators.

Traditional moving averages create lag to achieve smoothing. Laguerre Filter achieves smoothing AND responsiveness simultaneously. Used as preprocessing step, it cleans data for cleaner indicator signals. Instead of noisy RSI or MACD, feed them Laguerre-filtered price first. Game-changing for indicator accuracy with minimal lag penalty.

Formula

Laguerre Filter uses polynomial basis orthogonal functions:

1. Define Laguerre Polynomials

L₀ = e^(-x) L₁ = e^(-x) * (1 - x) L₂ = e^(-x) * (1 - 2x + x²/2)

Basis functions emphasizing recent data

2. Apply Gamma Coefficient

Gamma = decay factor (0.1 to 0.9) Recent weight dominates as gamma increases

Controls balance between recent and historical

3. Recursive Filtering

Filtered[n] = gamma*Price[n] + (1-gamma)*Filtered[n-1] Apply multiple passes for stronger smoothing

Exponential weighting with minimal lag

4. Output Filtered Price

Laguerre_Price = Filtered[n] Ultra-smooth price series ready for indicators

Cleaner input for RSI, MACD, Bollinger calculations

Interpretation

Laguerre output is smoothed price, not impulse indicator

Use as input to other indicators for cleaner output

Gamma 0.5 = balanced smoothing and responsiveness

Gamma 0.9 = maximum smoothing, more lag

Gamma 0.1 = responsive but less smoothing benefit

Parameters

Parameter	Type	Default	Description
gamma	number	0.5	Decay coefficient for recent weighting.
passes	number	2	Multiple filter passes for smoothing.
source	Node	Auto	The root data source node.

💡 Tip: Gamma 0.5 works for most charts. Increase passes (3-4) for extra smoothing on noisy data. Use as intermediate node feeding into RSI or MACD for cleaner output. Higher passes = more lag but better smoothing.

Common Use Cases

1. Preprocessing for Indicators

Instead of RSI on raw price, apply Laguerre Filter to price, then feed filtered price to RSI. Result: beautifully smooth RSI without whipsaws, still responsive. Same for MACD, Stochastic, momentum indicators. Universally applicable preprocessor.

2. Trend Line Construction

Draw trend lines on Laguerre-filtered price instead of raw price. Lines become much cleaner with fewer zigzags. Same trend structure with less noise. Perfect for technical analysis that relies on clear price trends.

3. Moving Average Crossovers

All moving average strategies work better on Laguerre-filtered price. No lag penalty (Laguerre is already smooth), but cleaner crossovers. Replace raw MA signals with Laguerre-MA signals for higher win rate.

4. Support & Resistance Level Building

Identify highs/lows on filtered price chart. Keeps only significant reversals, filters out micro-structure noise. Creates more reliable S/R zones with fewer touch points to noise.

Advantages & Limitations

✓

Advantages

Minimal lag with maximum smoothing
Mathematically optimal polynomial basis
Cleaner downstream indicators
No lag penalty like EMA/SMA
Improves all indicator performance

Limitations

Complex mathematical basis (not intuitive)
Multiple passes add processing load
Not a standalone indicator
Requires understanding of downstream use
Platform support limited (advanced feature)

Tips & Best Practices

💡 Use as Preprocessing Layer

Never standalone. Always feed output to other indicators (RSI, MACD, moving averages). Think of it as data preparation step, not trading signal generator. Utility function, not decision maker.

📊 Tune Gamma per Instrument

Crypto volatile = gamma 0.6-0.7 for responsiveness. Stocks trending = gamma 0.4-0.5 for smoothing. Forex choppy = gamma 0.7-0.8. Backtest different values to find sweet spot for your asset class.

⚡ Monitor Original Alongside Filtered

Display both raw price and Laguerre-filtered price on chart. When they diverge sharply, something moved significantly. Distance between them = noise elimination factor. Very smooth = lots of chop being filtered.

⚠️ Watch for Over-Smoothing

Too many passes (4+) with low gamma = missing real moves. Filtered price becomes detached from reality. Balance smoothing benefit against responsiveness loss. 2 passes standard, 3 maximum for most uses.

Example Strategy

Laguerre Filter + RSI preprocessor strategy:

Laguerre-Filtered RSI Trade

1Preprocessing Phase

Apply Laguerre Filter to close prices
Use gamma 0.5, passes 2 (standard settings)
Feed filtered price to RSI calculation

2Entry Signal

Laguerre-RSI drops below 30 (oversold)
Expect mean reversion bounce
Enter long position on confirmation

3Exit Condition

Laguerre-RSI rises above 70 (overbought)
Take profits at target (usually 2-3%)
Or hold for trend reversal below 50

4Risk Rules

Stop below recent low + 1 ATR
Laguerre-RSI less whipsaw = can hold larger winners
Risk 1.5-2% per trade, hold for 3-5% targets

Related Nodes

Laguerre RSI

RSI preprocessed with Laguerre filtering.

Fisher Transform

Similar polynomial-based preprocessing filter.

RSI

Downstream indicator for Laguerre output.

Trend Indicators

Further processing of filtered data.

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