The Kalman Filter is an optimal algorithm used for smoothing data by balancing predicted values and actual measured values. In this indicator, the Kalman Filter is applied to smooth price data, with the flexibility to choose the input data (e.g., close, open, high, or low prices). This customization allows users to tailor the analysis to their specific needs.
1. Overall Objective
The primary goals of the Kalman Filter are:
- Reduce noise in price data: Eliminate random fluctuations to produce a more stable signal.
- Detect trends: Highlight market trends by combining predictions (from dynamic models) with actual measurements (customizable input data).
2. Step-by-Step Process
Step 1: Initialization
The Kalman Filter starts with the following initial values:
- Estimate (Current State): The initial state is set to the first value in the data series (e.g., the first closing price or any user-selected input).
- Prediction Error: Initialized with a high value, reflecting the initial uncertainty of the system.
- Measurement Error: Proportional to the smoothing period. A longer period implies greater measurement error, reflecting that the data is less reliable.
Step 2: Predict the Next State
In this step, the Kalman Filter predicts the next state based on the current state:
- Predicted Value: Derived from the current estimated state.
- Prediction Error: Remains largely unchanged at this stage, as no new data has been introduced yet.
Step 3: Compute the Kalman Gain
The Kalman Gain is a weight that determines the influence of the predicted value versus the measured value. It is calculated using the formula:
- Significance:
- If Measurement Error is small (reliable data), the Kalman Gain is high, meaning the measured value has a greater influence.
- If Prediction Error is small (accurate prediction), the Kalman Gain is low, meaning the prediction carries more weight.
Step 4: Update the Estimate
Using the Kalman Gain, the predicted value is adjusted based on the discrepancy between the actual measurement and the predicted value:
- Measurement Difference: This is the difference between the actual input value (e.g., the selected price type) and the predicted value.
- Kalman Gain: Determines how much the prediction should be corrected by the measurement.
Step 5: Update the Prediction Error
The prediction error is updated and gradually decreases over time, reflecting increasing confidence in the estimate:
- Process Noise: Reflects the uncertainty in the dynamic model and is adjusted based on the smoothing period.
- The result is a steadily decreasing error, improving the stability of the output signal.
3. How Kalman Filter Smooths Data in the Indicator
The Kalman Filter balances two sources of information:
- Predicted Value: The value derived from the previous state, representing a stable trend.
- Measured Value: The actual input data, which reflects the latest market conditions (e.g., user-selected price type).
- When the measured value is noisy (high Measurement Error), the smoothed value is less influenced by the measurement.
- When the measured value is stable (low Measurement Error), the smoothed value quickly adapts to the changes.
4. Specific Applications in the Indicator
- Customizable Input: Users can select the input data type (e.g., close, open, high, low, hl2, hlc3, ohlc4, … prices) depending on the analysis needs.
- Short- and Long-Term Signals: Two Kalman Filters are applied simultaneously for short and long smoothing periods:
- Short-Term: Reacts quickly to short-term market fluctuations.
- Long-Term: Detects more stable, long-term trends.
- Trend Detection: The comparison between the two Kalman Filter outputs determines the market trend:
- If the short-term signal is above the long-term signal, the trend is upward.
- If the short-term signal is below the long-term signal, the trend is downward.
5. Advantages of Kalman Filter in the Indicator
- Effective Smoothing: Reduces random noise in price data, producing a more stable output signal.
- Flexible Customization: The ability to choose input data enhances analysis versatility.
- Trend Detection: Combining short- and long-term signals provides a clear identification of upward or downward trends.
- Quick Adaptation: Continuous updates with new data ensure the smoothed signal reflects recent market changes.
6. Logic Summary
The Kalman Filter in this indicator works by balancing predictions (stability) and actual measurements (sensitivity to change). With customizable input options, users can optimize the trend detection process to suit their specific requirements. The Kalman Gain acts as a dynamic weight, ensuring that the output is both stable and responsive. The resulting smoothed signal provides a reliable foundation for identifying trends in financial markets.
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Download the Kalman Trend Levels Scanner indicator using the Kalman Filter logic above with integrated Scanner of currency pairs, time frames here:
– for MT5: Kalman Trend Levels MT5 Scanner
– for MT4: Kalman Trend Levels MT4 Scanner