Fiche publication
Date publication
juillet 2026
Journal
Entropy (Basel, Switzerland)
Auteurs
Membres identifiés du Cancéropôle Est :
Pr CLAUSEL Marianne
Tous les auteurs :
Hamzi B, Clausel M, Dingle K, Hutter M, Terry Jack M
Lien Pubmed
Résumé
Spurious correlations between time series are a persistent problem: simple, low-complexity patterns are abundant, so unrelated series can easily exhibit high Pearson correlation. We argue that Kolmogorov complexity-a series' resistance to compression-provides a principled diagnostic for flagging such cases. We prove an algorithmic trilemma: a pair of binary sequences cannot simultaneously be algorithmically independent, highly correlated, and highly complex. This gives a deterministic complexity ceiling for independent correlated pairs and a probabilistic bound under which spurious correlations among independent high-complexity pairs are exponentially rare; we further bridge these results to an effective Hausdorff dimension obstruction. These guarantees hold for binary sequences under Hamming correlation; their extension to real-valued series via serialisation and LZ compression is empirically validated rather than proved, so the joint indicator JLZ=min{C˜LZ(x),C˜LZ(y)} is a calibrated diagnostic, not a causal test. On two toy models-coupled logistic maps and multivariate fractional Brownian motion (dimH=2-H)-false positives are far more common among low-complexity series. Because noise inflates complexity and non-stationary processes can be both complex and spuriously correlated, we recommend a two-stage workflow: establish stationarity, then report JLZ alongside ρ.
Mots clés
Hausdorff dimension, Kolmogorov complexity, Lempel–Ziv complexity, algorithmic information theory, fractional Brownian motion, simplicity bias, spurious correlations, time series
Référence
Entropy (Basel). 2026 07 16;28(7):
