Kalman Momentum

Kalman Filter
The Kalman Filter is an algorithm used for recursive estimation and filtering of time-series data. It was developed by Rudolf E. Kálmán in the 1960s and has found widespread applications in various fields, including control systems, navigation, signal processing, and finance.

The primary purpose of the Kalman filter is to estimate the state of a dynamic system based on a series of noisy measurements over time. It operates recursively, meaning it processes each new measurement and updates its estimate of the system state as new data becomes available.

Kalman Momentum Indicator
This indicator implements the Kalman Filter to provide a smoothed momentum indicator using returns. The momentum in this indicator is calculated by getting the logarithmic returns and then getting the expected value.

The Kalman calculation in this indicator is used to filter and predict the next value based on the logarithmic returns expected value.

Here's a simplified explanation of the steps and how they are applied in the Script:

State Prediction: Predict the current state based on the previous state estimate.

Error Covariance Prediction: Predict the covariance of the prediction error.
Correction Step:

Kalman Gain Calculation: Calculate the Kalman gain, which determines the weight given to the measurement.

State Correction: Update the state estimate based on the measurement.

Error Covariance Correction: Update the error covariance.

In this Script, the Kalman Filter is applied to estimate the state of the system, with two state variables.

When the Kalman Momentum is above 0, there is positive momentum or positive smoothed expected value.

When the Kalman Momentum is below 0, there is negative momentum or negative smoothed expected value.

How to Use:

Trend Identification:
Positive values of the Kalman Momentum Indicator indicates positive expected value, while negative values suggest negative expected value.
You can look for changes in the sign of the indicator to identify potential shifts in market direction.
Volatility Analysis:
Observe the behavior of the indicator during periods of high and low volatility. Changes in the volatility of the Kalman Momentum Indicator may precede changes in market conditions.
Filtering Noise:
The Kalman Filter is known for its ability to filter out noise in time series data. Use the Kalman Momentum Indicator to filter out the noise in momentum to catch the trend more clearly.
Squeezes:
At time there may be squeezes, and these are zones with low volatility. What could follow after these zones are expansions and huge trending moves.

Indicator Settings:

You can change the source of the calculations.
There is also a lookback for the log returns.

Understanding Expected Value in Trading:
The Expected Value is a fundamental concept that shows the potential outcomes of a trading strategy or individual trade over a series of occurrences. It is a measure that represents the average outcome when a particular action is repeated multiple times.

Images of the indicator: