TASC 2025.12 The One Euro Filter

█ OVERVIEW

This script implements the One Euro filter, developed by Georges Casiez, Nicolas Roussel, and Daniel Vogel, and adapted by John F. Ehlers in his article "Low-Latency Smoothing" from the December 2025 edition of the TASC Traders' Tips. The original creators gave the filter its name to suggest that it is cheap and efficient, like something one might purchase for a single Euro.

█ CONCEPTS

The One Euro filter is an EMA-based low-pass filter that adapts its smoothing factor (alpha) based on the absolute values of smoothed rates of change in the source series. It was designed to filter noisy, high-frequency signals in real time with low latency. Ehlers simplifies the filter for market analysis by calculating alpha in terms of bar periods rather than time and frequency, because periods are naturally intuitive for a discrete financial time series.

In his article, Ehlers demonstrates how traders can apply the adaptive One Euro filter to a price series for simple low-latency smoothing. Additionally, he explains that traders can use the filter as a smoothed oscillator by applying it to a high-pass filter. In essence, similar to other low-pass filters, traders can apply the One Euro filter to any custom source to derive a smoother signal with reduced noise and low lag.

This script applies the One Euro filter to a specified source series, and it applies the filter to a two-pole high-pass filter or other oscillator, depending on the selected "Osc type" option. By default, it displays the filtered source series on the main chart pane, and it shows the oscillator and its filtered series in a separate pane.

█ INPUTS

• Source: The source series for the first filter and the selected oscillator.
  
• Min period: The minimum cutoff period for the smoothing calculation.
  
• Beta: Controls the responsiveness of the filter. The filter adds the product of this value and the smoothed source change to the minimum period to determine the filter's smoothing factor. Larger values cause more significant changes in the maximum cutoff period, resulting in a smoother response.
  
• Osc type: The type of oscillator to calculate for the pane display. By default, the indicator calculates a high-pass filter. If the selected type is "None", the indicator displays the "Source" series and its filtered result in a separate pane rather than showing the filter on the main chart. With this setting, users can pass plotted values from another indicator and view the filtered result in the pane.
  
• Period: The length for the selected oscillator's calculation.