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“Chaosometer: a market efficiency barometer”

An implementation of the efficiency score developed in Ardakani (2026). The application maps any return series to a scalar score between 0 and 100 measuring departure from the martingale hypothesis, using nonparametric mutual information rather than the Gaussian dependence measures common in the efficiency literature.

The estimator is nearest-neighbor based and imposes no distributional assumption, which matters for financial returns whose tail index frequently falls below the level at which variance-based tests remain valid. Dependence is decomposed into a level channel, capturing directional predictability, and a volatility channel, capturing conditional heteroskedasticity, with a Gaussian multi-lag baseline anchoring the scale across assets. A Hill tail-index estimate and a Ljung-Box statistic accompany each score.

Method: “Bayesian inference for market efficiency under heavy tails,” Applied Stochastic Models in Business and Industry, e70109. DOI: 10.1002/asmb.70109.

Documentation: Technical specification. States each formula and verifies it against the implementation.

Access: chaosometer.com. A free tier is available for academic and classroom use.