VWAP Kalman Filter

Overview
This indicator applies Kalman filtering techniques to Volume Weighted Average Price (VWAP) calculations, providing a statistically optimized approach to VWAP analysis. The Kalman filter reduces noise while maintaining responsiveness to genuine price movements, addressing common VWAP limitations in volatile or low-volume conditions.

Technical Implementation

Kalman Filter Mathematics
The indicator implements a state-space model for VWAP estimation:
- Prediction Step: x̂(k|k-1) = x̂(k-1|k-1) + v(k-1)
- Update Step: x̂(k|k) = x̂(k|k-1) + K(k)[z(k) - x̂(k|k-1)]
- Kalman Gain: K(k) = P(k|k-1) / (P(k|k-1) + R)

Where:
- x̂ = estimated VWAP state
- K = Kalman gain (adaptive weighting factor)
- P = error covariance
- R = measurement noise
- Q = process noise
- v = optional velocity component

Core Components

Dual VWAP System
- Standard VWAP: Traditional volume-weighted calculation
- Kalman-filtered VWAP: Noise-reduced estimation with optional velocity tracking
- Real-time divergence measurement between filtered and unfiltered values

Adaptive Filtering
- Process Noise (Q): Controls adaptation to price changes (0.001-1.0)
- Measurement Noise (R): Determines smoothing intensity (0.01-5.0)
- Optional velocity tracking for momentum-based filtering

Multi-Timeframe Anchoring
- Session, Weekly, Monthly, Quarterly, and Yearly anchor periods
- Automatic Kalman state reset on anchor changes
- Maintains VWAP integrity across timeframes

Features

Visual Components
- Dual VWAP Lines: Compare filtered vs. unfiltered in real-time
- Dynamic Bands: Three-level deviation bands (1σ, 2σ, 3σ)
- Trend Coloring: Automatic color adaptation based on price position
- Cloud Visualization: Highlights divergence between standard and Kalman VWAP
- Signal Markers: Crossover and band-touch indicators

Trading Signals
- VWAP crossover detection with Kalman filtering
- Band touch alerts at multiple standard deviation levels
- Velocity-based momentum confirmation (optional)
- Divergence warnings when filtered/unfiltered values separate

Information Display
- Real-time VWAP values (both standard and filtered)
- Trend direction indicator
- Velocity/momentum reading (when enabled)
- Divergence percentage calculation
- Anchor period display

Input Parameters

VWAP Settings
- Anchor Period: Choose calculation reset period
- Band Multipliers: Customize deviation band distances
- Display Options: Toggle standard VWAP and bands

Kalman Parameters
- Length: Base period for calculations (5-200)
- Process Noise (Q: Higher values increase responsiveness
- Measurement Noise (R): Higher values increase smoothing
- Velocity Tracking: Enable momentum-based filtering

Visual Controls
- Toggle filtered/unfiltered VWAP display
- Band visibility options
- Signal markers on/off
- Cloud fill between VWAPs
- Bar coloring by trend

Use Cases

Noise Reduction
Particularly effective during:
- Low volume periods (pre-market, lunch hours)
- Volatile market conditions
- Fast-moving markets where standard VWAP whipsaws

Trend Identification
- Cleaner trend signals with reduced false crosses
- Earlier trend detection through velocity component
- Confirmation through divergence analysis

Support/Resistance
- Filtered VWAP provides more stable S/R levels
- Bands adapt to filtered values for better zone identification
- Reduced false breakout signals

Technical Advantages

1. Optimal Estimation: Mathematically optimal under Gaussian noise assumptions
2. Adaptive Response: Self-adjusting to market conditions
3. Predictive Element: Velocity component provides forward-looking insight
4. Noise Immunity: Superior noise rejection vs. simple moving average smoothing

Limitations

- Assumes linear price dynamics
- Requires parameter optimization for different instruments
- May lag during sudden volatility regime changes
- Not suitable as standalone trading system

Mathematical Background

Based on control systems theory, the Kalman filter provides recursive Bayesian estimation originally developed for aerospace applications. This implementation adapts the algorithm specifically for financial time series, maintaining VWAP's volume-weighted properties while adding statistical filtering.

Comparison with Standard VWAP

Standard VWAP Issues Addressed:
- Choppy behavior in low volume
- Whipsaws around VWAP line
- Lag in trend identification
- Noise in deviation bands

Kalman VWAP Benefits:
- Smooth yet responsive line
- Fewer false signals
- Optional momentum tracking
- Statistically optimized filtering

Alert Conditions

The indicator includes several pre-configured alert conditions:
- Bullish/Bearish VWAP crosses
- Upper/Lower band touches
- High divergence warnings
- Velocity shifts (if enabled)

---

This open-source indicator is provided as-is for educational and trading purposes. No guarantees are made regarding trading performance. Users should conduct their own testing and validation before using in live trading.