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Published on: March 1, 2022
Time Series Correlations and Kolmogorov Complexity: A Hausdorff Dimension Perspective
Boumediene Hamzi1,2, Marianne Clausel3, Kamal Dingle4
1Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125, USA.
Entropy (Basel, Switzerland)
|July 28, 2026
Summary
Kolmogorov complexity, a measure of resistance to compression, can diagnose spurious correlations in time series data. This algorithmic approach helps identify unrelated series exhibiting high Pearson correlation, improving data analysis reliability.
Area of Science:
- Data Science
- Information Theory
- Time Series Analysis
Background:
- Spurious correlations are common in time series due to abundant simple patterns.
- High Pearson correlation does not always imply a true relationship between series.
Purpose of the Study:
- To introduce Kolmogorov complexity as a principled diagnostic for spurious correlations.
- To establish theoretical bounds for independent, correlated, and complex time series pairs.
Main Methods:
- Proving an algorithmic trilemma for binary sequences regarding independence, correlation, and complexity.
- Extending theoretical results to real-valued series using serialization and LZ compression (JLZ indicator).
- Empirical validation on coupled logistic maps and fractional Brownian motion models.
Main Results:
- A theoretical complexity ceiling is established for independent, correlated pairs.
- Spurious correlations among independent, high-complexity pairs are shown to be exponentially rare.
- The JLZ indicator is a calibrated diagnostic, with false positives more common in low-complexity series.
Conclusions:
- Kolmogorov complexity offers a robust method for detecting spurious correlations.
- A two-stage workflow involving stationarity assessment and JLZ reporting is recommended.
- The JLZ indicator, combined with Pearson correlation (ρ), enhances time series analysis accuracy.
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