Adaptive Kalman Trend Filter (Zeiierman)█ Overview
The Adaptive Kalman Trend Filter indicator is an advanced trend-following tool designed to help traders accurately identify market trends. Utilizing the Kalman Filter—a statistical algorithm rooted in control theory and signal processing—this indicator adapts to changing market conditions, smoothing price data to filter out noise. By focusing on state vector-based calculations, it dynamically adjusts trend and range measurements, making it an excellent tool for both trend-following and range-based trading strategies. The indicator's adaptive nature is enhanced by options for volatility adjustment and three unique Kalman filter models, each tailored for different market conditions.
█ How It Works
The Kalman Filter works by maintaining a model of the market state through matrices that represent state variables, error covariances, and measurement uncertainties. Here’s how each component plays a role in calculating the indicator’s trend:
⚪ State Vector (X): The state vector is a two-dimensional array where each element represents a market property. The first element is an estimate of the true price, while the second element represents the rate of change or trend in that price. This vector is updated iteratively with each new price, maintaining an ongoing estimate of both price and trend direction.
⚪ Covariance Matrix (P): The covariance matrix represents the uncertainty in the state vector’s estimates. It continuously adapts to changing conditions, representing how much error we expect in our trend and price estimates. Lower covariance values suggest higher confidence in the estimates, while higher values indicate less certainty, often due to market volatility.
⚪ Process Noise (Q): The process noise matrix (Q) is used to account for uncertainties in price movements that aren’t explained by historical trends. By allowing some degree of randomness, it enables the Kalman Filter to remain responsive to new data without overreacting to minor fluctuations. This noise is particularly useful in smoothing out price movements in highly volatile markets.
⚪ Measurement Noise (R): Measurement noise is an external input representing the reliability of each new price observation. In this indicator, it is represented by the setting Measurement Noise and determines how much weight is given to each new price point. Higher measurement noise makes the indicator less reactive to recent prices, smoothing the trend further.
⚪ Update Equations:
Prediction: The state vector and covariance matrix are first projected forward using a state transition matrix (F), which includes market estimates based on past data. This gives a “predicted” state before the next actual price is known.
Kalman Gain Calculation: The Kalman gain is calculated by comparing the predicted state with the actual price, balancing between the covariance matrix and measurement noise. This gain determines how much of the observed price should influence the state vector.
Correction: The observed price is then compared to the predicted price, and the state vector is updated using this Kalman gain. The updated covariance matrix reflects any adjustment in uncertainty based on the latest data.
█ Three Kalman Filter Models
Standard Model: Assumes that market fluctuations follow a linear progression without external adjustments. It is best suited for stable markets.
Volume Adjusted Model: Adjusts the filter sensitivity based on trading volume. High-volume periods result in stronger trends, making this model suitable for volume-driven assets.
Parkinson Adjusted Model: Uses the Parkinson estimator, accounting for volatility through high-low price ranges, making it effective in markets with high intraday fluctuations.
These models enable traders to choose a filter that aligns with current market conditions, enhancing trend accuracy and responsiveness.
█ Trend Strength
The Trend Strength provides a visual representation of the current trend's strength as a percentage based on oscillator calculations from the Kalman filter. This table divides trend strength into color-coded segments, helping traders quickly assess whether the market is strongly trending or nearing a reversal point. A high trend strength percentage indicates a robust trend, while a low percentage suggests weakening momentum or consolidation.
█ Trend Range
The Trend Range section evaluates the market's directional movement over a specified lookback period, highlighting areas where price oscillations indicate a trend. This calculation assesses how prices vary within the range, offering an indication of trend stability or the likelihood of reversals. By adjusting the trend range setting, traders can fine-tune the indicator’s sensitivity to longer or shorter trends.
█ Sigma Bands
The Sigma Bands in the indicator are based on statistical standard deviations (sigma levels), which act as dynamic support and resistance zones. These bands are calculated using the Kalman Filter's trend estimates and adjusted for volatility (if enabled). The bands expand and contract according to market volatility, providing a unique visualization of price boundaries. In high-volatility periods, the bands widen, offering better protection against false breakouts. During low volatility, the bands narrow, closely tracking price movements. Traders can use these sigma bands to spot potential entry and exit points, aiming for reversion trades or trend continuation setups.
Trend Based
Volatility Based
█ How to Use
Trend Following:
When the Kalman Filter is green, it signals a bullish trend, and when it’s red, it indicates a bearish trend. The Sigma Cloud provides additional insights into trend strength. In a strong bullish trend, the cloud remains below the Kalman Filter line, while in a strong bearish trend, the cloud stays above it. Expansion and contraction of the Sigma Cloud indicate market momentum changes. Rapid expansion suggests an impulsive move, which could either signal the continuation of the trend or be an early sign of a possible trend reversal.
Mean Reversion: Watch for prices touching the upper or lower sigma bands, which often act as dynamic support and resistance.
Volatility Breakouts: Enable volatility-adjusted sigma bands. During high volatility, watch for price movements that extend beyond the bands as potential breakout signals.
Trend Continuation: When the Kalman Filter line aligns with a high trend strength, it signals a continuation in that direction.
█ Settings
Measurement Noise: Adjusts how sensitive the indicator is to price changes. Higher values smooth out fluctuations but delay reaction, while lower values increase sensitivity to short-term changes.
Kalman Filter Model: Choose between the standard, volume-adjusted, and Parkinson-adjusted models based on market conditions.
Band Sigma: Sets the standard deviation used for calculating the sigma bands, directly affecting the width of the dynamic support and resistance.
Volatility Adjusted Bands: Enables bands to dynamically adapt to volatility, increasing their effectiveness in fluctuating markets.
Trend Strength: Defines the lookback period for trend strength calculation. Shorter periods result in more responsive trend strength readings, while longer periods smooth out the calculation.
Trend Range: Specifies the lookback period for the trend range, affecting the assessment of trend stability over time.
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Disclaimer
The information contained in my Scripts/Indicators/Ideas/Algos/Systems does not constitute financial advice or a solicitation to buy or sell any securities of any type. I will not accept liability for any loss or damage, including without limitation any loss of profit, which may arise directly or indirectly from the use of or reliance on such information.
All investments involve risk, and the past performance of a security, industry, sector, market, financial product, trading strategy, backtest, or individual's trading does not guarantee future results or returns. Investors are fully responsible for any investment decisions they make. Such decisions should be based solely on an evaluation of their financial circumstances, investment objectives, risk tolerance, and liquidity needs.
My Scripts/Indicators/Ideas/Algos/Systems are only for educational purposes!
Adaptivekalman
Adaptive Kalman filter - Trend Strength Oscillator (Zeiierman)█ Overview
The Adaptive Kalman Filter - Trend Strength Oscillator by Zeiierman is a sophisticated trend-following indicator that uses advanced mathematical techniques, including vector and matrix operations, to decompose price movements into trend and oscillatory components. Unlike standard indicators, this model assumes that price is driven by two latent (unobservable) factors: a long-term trend and localized oscillations around that trend. Through a dynamic "predict and update" process, the Kalman Filter leverages vectors to adaptively separate these components, extracting a clearer view of market direction and strength.
█ How It Works
This indicator operates on a trend + local change Kalman Filter model. It assumes that price movements consist of two underlying components: a core trend and an oscillatory term, representing smaller price fluctuations around that trend. The Kalman Filter adaptively separates these components by observing the price series over time and performing real-time updates as new data arrives.
Predict and Update Procedure: The Kalman Filter uses an adaptive predict-update cycle to estimate both components. This cycle allows the filter to adjust dynamically as the market evolves, providing a smooth yet responsive signal. The trend component extracted from this process is plotted directly, giving a clear view of the prevailing direction. The oscillatory component indicates the tendency or strength of the trend, reflected in the green/red coloration of the oscillator line.
Trend Strength Calculation: Trend strength is calculated by comparing the current oscillatory value against a configurable number of past values.
█ Three Kalman filter Models
This indicator offers three distinct Kalman filter models, each designed to handle different market conditions:
Standard Model: This is a conventional Kalman Filter, balancing responsiveness and smoothness. It works well across general market conditions.
Volume-Adjusted Model: In this model, the filter’s measurement noise automatically adjusts based on trading volume. Higher volumes indicate more informative price movements, which the filter treats with higher confidence. Conversely, low-volume movements are treated as less informative, adding robustness during low-activity periods.
Parkinson-Adjusted Model: This model adjusts measurement noise based on price volatility. It uses the price range (high-low) to determine the filter’s sensitivity, making it ideal for handling markets with frequent gaps or spikes. The model responds with higher confidence in low-volatility periods and adapts to high-volatility scenarios by treating them with more caution.
█ How to Use
Trend Detection: The oscillator oscillates around zero, with positive values indicating a bullish trend and negative values indicating a bearish trend. The further the oscillator moves from zero, the stronger the trend. The Kalman filter trend line on the chart can be used in conjunction with the oscillator to determine the market's trend direction.
Trend Reversals: The blue areas in the oscillator suggest potential trend reversals, helping traders identify emerging market shifts. These areas can also indicate a potential pullback within the prevailing trend.
Overbought/Oversold: The thresholds, such as 70 and -70, help identify extreme conditions. When the oscillator reaches these levels, it suggests that the trend may be overextended, possibly signaling an upcoming reversal.
█ Settings
Process Noise 1: Controls the primary level of uncertainty in the Kalman filter model. Higher values make the filter more responsive to recent price changes, but may also increase susceptibility to random noise.
Process Noise 2: This secondary noise setting works with Process Noise 1 to adjust the model's adaptability. Together, these settings manage the uncertainty in the filter's internal model, allowing for finely-tuned adjustments to smoothness versus responsiveness.
Measurement Noise: Sets the uncertainty in the observed price data. Increasing this value makes the filter rely more on historical data, resulting in smoother but less reactive filtering. Lower values make the filter more responsive but potentially more prone to noise.
O sc Smoothness: Controls the level of smoothing applied to the trend strength oscillator. Higher values result in a smoother oscillator, which may cause slight delays in response. Lower values make the oscillator more reactive to trend changes, useful for capturing quick reversals or volatility within the trend.
Kalman Filter Model: Choose between Standard, Volume-Adjusted, and Parkinson-Adjusted models. Each model adapts the Kalman filter for specific conditions, whether balancing general market data, adjusting based on volume, or refining based on volatility.
Trend Lookback: Defines how far back to look when calculating the trend strength, which impacts the indicator's sensitivity to changes in trend strength. Shorter values make the oscillator more reactive to recent trends, while longer values provide a smoother reading.
Strength Smoothness: Adjusts the level of smoothing applied to the trend strength oscillator. Higher values create a more gradual response, while lower values make the oscillator more sensitive to recent changes.
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Disclaimer
The information contained in my Scripts/Indicators/Ideas/Algos/Systems does not constitute financial advice or a solicitation to buy or sell any securities of any type. I will not accept liability for any loss or damage, including without limitation any loss of profit, which may arise directly or indirectly from the use of or reliance on such information.
All investments involve risk, and the past performance of a security, industry, sector, market, financial product, trading strategy, backtest, or individual's trading does not guarantee future results or returns. Investors are fully responsible for any investment decisions they make. Such decisions should be based solely on an evaluation of their financial circumstances, investment objectives, risk tolerance, and liquidity needs.
My Scripts/Indicators/Ideas/Algos/Systems are only for educational purposes!
