OPEN-SOURCE SCRIPT
Kalman Quantum Drift [JOAT]
KALMAN QUANTUM DRIFT [JOAT]
A trend-and-envelope engine built on the cleanest pair of state-space tools in quantitative finance: a Kalman filter for the centreline (Bayesian, adaptive, mathematically optimal under linear-Gaussian assumptions) and a GARCH(1,1) conditional-variance model for the envelope (the institutional standard for time-varying volatility). The script reads price as a noisy observation of an unobservable true state; the Kalman filter estimates that state recursively; GARCH estimates the noise's volatility; the envelope = mid ± k · σ_GARCH. A signal engine layered on top detects Collapse events (>3σ excursions) and Tunnel events (gap-throughs of the envelope) — the quantum analogues of state collapse and quantum tunnelling.
The Kalman filter, properly
A single-state recursive Bayesian filter. At each bar:
The two tuning knobs are:
This is the Bayesian-optimal smoother for linear-Gaussian state-space data. Real markets are not perfectly linear-Gaussian, but the Kalman estimate is robust enough to be the cleanest mid-line you can build without going into heavy non-linear filtering.
GARCH(1,1) envelope
The envelope around the Kalman mid is not ATR or stdev — it is GARCH(1,1):
σ²_t = ω + α · ε²_{t−1} + β · σ²_{t−1}
ω is the long-run variance baseline, α is the reaction to last shock squared (ARCH term), β is the persistence of past variance (GARCH term). For stationarity, α + β < 1 (the script's α/β defaults respect that). Optional log returns (default ON) and a warm-up window seed the variance from realised returns.
The envelope is mid ± k · σ_GARCH, rendered as a gradient (configurable number of nested fills, each at progressive transparency from edge to core).
Three-signal engine
A configurable signal cooldown (default 5 bars) prevents stacking.
Visual system
A locked Quantum palette (cyan bull / pink bear / muted cyan mid on a deep violet-black) gives the chart a distinctive quant-physics identity.
Dashboard
Monospaced table positionable to any of nine corners. Surfaces:
Alerts
Six alert conditions, each independently controllable:
How to read it
Three reads, in order of conviction:
Suggested settings
Defaults (Q = 0.02, R = 1.5, GARCH ω=2e-6 / α=0.10 / β=0.85, k = 2.5, gradient steps 6) are tuned for 15m–1H on liquid markets. For lower timeframes drop k to 2.0. For HTF raise R to 3.0 (more model trust on smoother data). The GARCH α/β defaults are the institutional standard; α + β remains under 1 for stationarity.
Originality
Kalman filtering and GARCH(1,1) are textbook quantitative-finance methods — both decades-old, both well-documented. The implementation here — the single-state recursive Kalman with exposed Q/R, the GARCH(1,1) variance recursion with warm-up window, the gradient-envelope render using strict two-hue alpha-only variation, the three-signal engine (Collapse / Tunnel / Cross), the optional Collapse-confirmed Buy/Sell gating, the event glyph markers, and the background tint on extremes — is JOAT-original. No third-party code reused. The pairing of Kalman + GARCH + quantum-inspired signal naming is the original presentation.
Limitations
The Kalman filter assumes linear-Gaussian state dynamics — real markets violate this, especially around news and gaps. The Q / R tuning is exposed precisely because no single setting is universally correct; tune to your instrument's noise profile. GARCH's α/β must sum to less than 1 for stationarity — the defaults respect this; if you push them too aggressively the variance can explode. Collapse and Tunnel events are confirmed on bar close (non-repainting).
—
-made with passion by jackofalltrades
A trend-and-envelope engine built on the cleanest pair of state-space tools in quantitative finance: a Kalman filter for the centreline (Bayesian, adaptive, mathematically optimal under linear-Gaussian assumptions) and a GARCH(1,1) conditional-variance model for the envelope (the institutional standard for time-varying volatility). The script reads price as a noisy observation of an unobservable true state; the Kalman filter estimates that state recursively; GARCH estimates the noise's volatility; the envelope = mid ± k · σ_GARCH. A signal engine layered on top detects Collapse events (>3σ excursions) and Tunnel events (gap-throughs of the envelope) — the quantum analogues of state collapse and quantum tunnelling.
The Kalman filter, properly
A single-state recursive Bayesian filter. At each bar:
- Predict: prior estimate = previous estimate. Prior variance = previous variance + Q.
- Update: Kalman gain = prior variance / (prior variance + R). New estimate = prior + gain × (observation − prior). New variance = (1 − gain) × prior variance.
The two tuning knobs are:
- Q (process noise) — how much the script trusts new observations. Higher Q = faster, noisier mid-line.
- R (measurement noise) — how much the script trusts the model. Higher R = slower, smoother mid-line.
This is the Bayesian-optimal smoother for linear-Gaussian state-space data. Real markets are not perfectly linear-Gaussian, but the Kalman estimate is robust enough to be the cleanest mid-line you can build without going into heavy non-linear filtering.
GARCH(1,1) envelope
The envelope around the Kalman mid is not ATR or stdev — it is GARCH(1,1):
σ²_t = ω + α · ε²_{t−1} + β · σ²_{t−1}
ω is the long-run variance baseline, α is the reaction to last shock squared (ARCH term), β is the persistence of past variance (GARCH term). For stationarity, α + β < 1 (the script's α/β defaults respect that). Optional log returns (default ON) and a warm-up window seed the variance from realised returns.
The envelope is mid ± k · σ_GARCH, rendered as a gradient (configurable number of nested fills, each at progressive transparency from edge to core).
Three-signal engine
- Collapse — fires when price travels more than collapse threshold (default 3.0) σ-units from the Kalman mid. The "state collapse" event — price has decisively departed the filter's expected band. Bull or bear depending on direction.
- Tunnel — fires when a bar gaps through the entire envelope from one side to the other. The "quantum tunnel" event — a discontinuous jump that bypasses the band gradient.
- Buy / Sell crosses — fire when price crosses the Kalman mid from one side. Optional Collapse confirmation gate (default ON) — Buy / Sell only fires when a Collapse occurred within the configurable lookback window. This dramatically improves signal quality.
A configurable signal cooldown (default 5 bars) prevents stacking.
Visual system
- Kalman mid-line — coloured by its own slope (bull / bear), configurable width.
- Gradient envelope — nested fills (configurable steps, default 6) using the same base hue with progressive transparency from edge to core. Strict two-hue discipline (bull cyan / bear pink only).
- Price bar colouring by mid slope (toggleable).
- Background tint on extremes — subtle bgcolor when price is at envelope edge (toggleable, default 92 transparency).
- Event glyphs — C (Collapse) and T (Tunnel) markers at the event bar. Configurable size.
A locked Quantum palette (cyan bull / pink bear / muted cyan mid on a deep violet-black) gives the chart a distinctive quant-physics identity.
Dashboard
Monospaced table positionable to any of nine corners. Surfaces:
- Current Kalman mid value with slope direction.
- σ_GARCH value and the envelope half-width.
- Distance of price from mid in σ-units.
- Last Collapse / Tunnel / Buy / Sell event with bar age.
- Q / R settings in use.
- GARCH ω / α / β confirmation.
Alerts
Six alert conditions, each independently controllable:
- Collapse Up / Down (>kσ excursion)
- Tunnel Up / Down (envelope gap-through)
- Slope Flip (Kalman mid changes direction)
- Sigma Spike (σ_GARCH exceeds its own recent baseline)
How to read it
Three reads, in order of conviction:
- Buy/Sell after a Collapse (the script's intended signal) — the cleanest trend-entry the engine produces. A Collapse means price decisively departed expected range; the subsequent mid-line cross confirms the new direction with the strongest possible context. This is the highest-conviction read.
- Tunnel — an exceptional, rare event. When a single bar jumps the entire envelope, the market has experienced a discontinuity (news, large block, exchange dislocation). Often produces the day's largest moves; almost always followed by elevated volatility.
- σ Spike alert without a directional event — a regime warning. Volatility just expanded without a directional commitment yet. The next signal that fires is statistically more likely to be meaningful than the one before the spike.
Suggested settings
Defaults (Q = 0.02, R = 1.5, GARCH ω=2e-6 / α=0.10 / β=0.85, k = 2.5, gradient steps 6) are tuned for 15m–1H on liquid markets. For lower timeframes drop k to 2.0. For HTF raise R to 3.0 (more model trust on smoother data). The GARCH α/β defaults are the institutional standard; α + β remains under 1 for stationarity.
Originality
Kalman filtering and GARCH(1,1) are textbook quantitative-finance methods — both decades-old, both well-documented. The implementation here — the single-state recursive Kalman with exposed Q/R, the GARCH(1,1) variance recursion with warm-up window, the gradient-envelope render using strict two-hue alpha-only variation, the three-signal engine (Collapse / Tunnel / Cross), the optional Collapse-confirmed Buy/Sell gating, the event glyph markers, and the background tint on extremes — is JOAT-original. No third-party code reused. The pairing of Kalman + GARCH + quantum-inspired signal naming is the original presentation.
Limitations
The Kalman filter assumes linear-Gaussian state dynamics — real markets violate this, especially around news and gaps. The Q / R tuning is exposed precisely because no single setting is universally correct; tune to your instrument's noise profile. GARCH's α/β must sum to less than 1 for stationarity — the defaults respect this; if you push them too aggressively the variance can explode. Collapse and Tunnel events are confirmed on bar close (non-repainting).
—
-made with passion by jackofalltrades
Script de código abierto
Fiel al espíritu de TradingView, el creador de este script lo ha convertido en código abierto, para que los traders puedan revisar y verificar su funcionalidad. ¡Enhorabuena al autor! Aunque puede utilizarlo de forma gratuita, recuerde que cualquier republicación del código está sujeta a nuestras Normas internas.
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Script de código abierto
Fiel al espíritu de TradingView, el creador de este script lo ha convertido en código abierto, para que los traders puedan revisar y verificar su funcionalidad. ¡Enhorabuena al autor! Aunque puede utilizarlo de forma gratuita, recuerde que cualquier republicación del código está sujeta a nuestras Normas internas.
The AI Trading Ecosystem, Built to win trades 📈
Get Full Access 👇
jackofalltrades.vip 🌐
t.me/jackofalltradesvip 🃏
Get Full Access 👇
jackofalltrades.vip 🌐
t.me/jackofalltradesvip 🃏
Exención de responsabilidad
La información y las publicaciones no constituyen, ni deben considerarse como, asesoramiento o recomendaciones financieras, de inversión, de trading u otro tipo, proporcionadas o respaldadas por TradingView. Obtenga más información en Condiciones de uso.