Relative Momentum Index with Laguerre Filter

The Relative Momentum Index
The Relative Momentum Index (RMI) is an oscillator that is a variation of the Relative Strength Index (RSI), but incorporates momentum over a variable lookback period rather than just consecutive price changes, which can help identify reversals and filter out noise.
It measures the momentum of price changes over a specified period, rather than just the magnitude of price changes like the RSI does.

• It counts up and down days from the current closing price relative to the closing price a certain number of days ago (e.g. 5 days ago), instead of just comparing consecutive daily closes like the RSI
  
• It is calculated by taking the ratio of the average upward price changes to the average downward price changes over a given period, where each change is measured from the close X days ago (X is the “momentum” period)
  
• Like the RSI, the RMI oscillates between 0 and 100, with readings above 70 considered overbought and below 30 oversold.
  
• In trending markets, the RMI tends to remain in overbought or oversold territory for extended periods. In trading ranges, it oscillates more predictably between the overbought and oversold levels.
  
• The RMI is generally considered better than the RSI at identifying potential reversal points, as it incorporates a momentum factor rather than just strength.
  
• It can be used in a similar way to the RSI for trade signals, such as buying when it rises above 30 from below, or selling when it falls below 70 from above
  

The Laguerre filter
A Laguerre filter is a type of infinite impulse response (IIR) filter used for smoothing signals or data. The Laguerre filter provides a way to apply variable smoothing to a signal by adjusting its pole position, allowing you to control the balance between smoothness and lag based on your preferences. It is an alternative to simple moving averages that can better preserve the shape of the original signal.