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Laguerre Timeframe Oscillator

Laguerre Timeframe Breadth Oscillator

Multi-timeframe × multi-gamma Laguerre breadth model

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Usage Notes
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• This is a regime & consensus indicator, not a trigger
• Best used for trend validation and risk filtering
• Extreme values tend to persist during strong regimes

This indicator answers a single question:

“Out of 198 independent Laguerre filters, how many are currently rising?”

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Concept
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Using Laguerre polynomials, we aggregate price behavior across:
• 11 explicit timeframes (1-minute → 1-day)
• 18 gamma responsiveness levels (0.10 → 0.95)

This produces 198 independent Laguerre curves.

The final oscillator is NOT price.
It represents a directional consensus across timescales and smoothing sensitivities.

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Laguerre Filter Mathematics
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For each Laguerre line i:

L0ᵢ(t) = (1 − γᵢ) · x(t) + γᵢ · L0ᵢ(t−1)
L1ᵢ(t) = −γᵢ · L0ᵢ(t) + L0ᵢ(t−1) + γᵢ · L1ᵢ(t−1)
L2ᵢ(t) = −γᵢ · L1ᵢ(t) + L1ᵢ(t−1) + γᵢ · L2ᵢ(t−1)
L3ᵢ(t) = −γᵢ · L2ᵢ(t) + L2ᵢ(t−1) + γᵢ · L3ᵢ(t−1)

Smoothed output:

Yᵢ(t) = ( L0ᵢ + 2·L1ᵢ + 2·L2ᵢ + L3ᵢ ) / 6

This weighted sum smooths noise while preserving phase better than a traditional EMA.

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Gamma Responsiveness
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Gamma controls responsiveness vs stability:

0.10 — Very fast, noisy
0.40 — Momentum-sensitive
0.70 — Trend-stable
0.95 — Very slow, structural

Each timeframe is evaluated across all gamma levels.

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Timeframes Used (11)
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Minutes: 1, 3, 5, 10, 15, 30, 45
Hours: 1, 2, 4
Days: 1

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Direction Test
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Each Laguerre line votes “up” or “down”:

Iᵢ(t) = 1 if Yᵢ(t) > Yᵢ(t−1)
Iᵢ(t) = 0 otherwise

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Breadth Calculation
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greenCount(t) =
I₁(t) + I₂(t) + I₃(t) + … + I₁₉₈(t)

Total number of rising Laguerre filters.

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Centered Breadth Oscillator
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oscRaw(t) = greenCount(t) − 99

(99 = half of 198; zero represents balanced breadth)

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Smoothing & Amplification
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EMA smoothing:
oscSmooth(t) = EMA₁₀₀(oscRaw)

Extreme emphasis:
oscExtreme(t) = 2 · oscSmooth(t)

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Clamped Final Output
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osc(t) = max( −99 , min( 99 , oscExtreme(t) ) )

Range:
• −99 → all filters falling
• 0 → mixed / neutral
• +99 → all filters rising

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Optional Probabilistic Interpretation
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p(t) = greenCount(t) / 198

Interpretable as the probability of upward directional alignment.

Reach out on Discord if you need further guidance. - Coño Vista

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