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A Novel Approach to Speed Up Hampel Filter for Outlier Detection.

Mario Roos-Hoefgeest Toribio1, Alejandro Garnung Menéndez1, Sara Roos-Hoefgeest Toribio1

  • 1Department of Electrical, Computer Electronics and Systems Engineering, University of Oviedo, 33003 Oviedo, Spain.

Sensors (Basel, Switzerland)
|September 19, 2025
PubMed
Summary

This study introduces a faster Hampel filter for time series outlier detection. The new method uses a modified Median Absolute Deviation (mMAD) for improved efficiency in large-scale and real-time applications.

Keywords:
Hampel filtermedian absolute deviation (MAD)outlier detectionreal-time filteringsignal processing

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Area of Science:

  • Data Science
  • Signal Processing
  • Statistical Analysis

Background:

  • Outlier detection is crucial for time series data quality and analysis.
  • The Hampel filter is a common method but computationally intensive due to Median Absolute Deviation (MAD) calculation.
  • High computational complexity limits Hampel filter application in large-scale and real-time scenarios.

Purpose of the Study:

  • To develop a computationally efficient variant of the Hampel filter.
  • To maintain the statistical robustness of outlier detection.
  • To enable real-time and large-scale time series processing.

Main Methods:

  • Proposed a novel Hampel filter variant replacing MAD with a computationally efficient estimator (mMAD).
  • Analyzed the computational complexity reduction from O(N·wlogw) to O(N·w).
  • Evaluated the variant's performance in outlier detection and processing time.

Main Results:

  • The proposed Hampel filter variant achieves a significant reduction in computational complexity.
  • The mMAD estimator retains the statistical robustness of the original MAD.
  • The variant demonstrates lower processing time and resource consumption compared to the standard Hampel filter.

Conclusions:

  • The novel Hampel filter variant offers a computationally efficient alternative for robust time series outlier detection.
  • This advancement is particularly beneficial for large-scale and real-time data analysis.
  • The method preserves outlier detection accuracy while enhancing processing efficiency.