A statistical test of market efficiency based on information theory

TL;DR

This paper introduces a statistical test for market efficiency using Shannon entropy to measure information in price return time series, applicable across various financial assets.

Contribution

It develops a novel entropy-based statistical test for market efficiency and derives its distribution under the efficient market hypothesis.

Findings

The test can reject market efficiency at specific dates.

It is applicable to stock indices, individual stocks, and cryptocurrencies.

Provides a method to assess market efficiency dynamically.

Abstract

We determine the amount of information contained in a time series of price returns at a given time scale, by using a widespread tool of the information theory, namely the Shannon entropy, applied to a symbolic representation of this time series. By deriving the exact and the asymptotic distribution of this market information indicator in the case where the efficient market hypothesis holds, we develop a statistical test of market efficiency. We apply it to a real dataset of stock indices, single stock, and cryptocurrency, for which we are able to determine at each date whether the efficient market hypothesis is to be rejected, with respect to a given confidence level.