Easily adaptable complexity measure for finite time series

Area of Science:

• Complexity Science
• Time Series Analysis
• Information Theory

Background:

• Traditional complexity measures often conflict and fail to satisfy all desired criteria.
• Kolmogorov complexity is typically associated with randomness, not a general complexity measure.
• Existing methods struggle with noise and transformations.

Purpose of the Study:

• To introduce a novel complexity measure for finite time series.
• To develop a measure that is invariant to monotonic transformations and robust to noise.
• To reconcile conflicting criteria for complexity measurement.

Main Methods:

• The proposed measure is derived from Kolmogorov complexity.
• It is designed to be invariant under monotonic transformations.
• The method demonstrates robustness against noise in time series data.

Main Results:

• A new complexity measure satisfying multiple, often conflicting, criteria is presented.
• The measure shows invariance to monotonic transformations.
• The approach offers robustness against noise, enhancing its practical applicability.

Conclusions:

• The developed complexity measure provides a versatile tool for analyzing time series.
• This work potentially bridges symbolic dynamics and permutation dynamics.
• The findings offer a new perspective on applying Kolmogorov complexity for broader measures.