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Entropy and Efficiency of the ETF Market

Calcagnile, L. M., Corsi, F. ORCID: 0000-0003-2683-4479 & Marmi, S. (2019). Entropy and Efficiency of the ETF Market. Computational Economics, 55(1), pp. 143-184. doi: 10.1007/s10614-019-09885-z


We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-min and 5-min price time series of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a methodology to isolate residual inefficiencies from other sources of regularities, such as the intraday pattern, the volatility clustering and the microstructure effects. The first two are modelled as multiplicative factors, while the microstructure is modelled as an ARMA noise process. Following an analytical and empirical combined approach, we find a strong relationship between low entropy and high relative tick size and that volatility is responsible for the largest amount of regularity, averaging 62% of the total regularity against 18% of the intraday pattern regularity and 20% of the microstructure.

Publication Type: Article
Additional Information: This is a pre-print of an article published in Computational Economics. The final authenticated version is available online at:
Publisher Keywords: Market efficiency, Shannon entropy, Information theory, ARMA processes
Subjects: H Social Sciences > HB Economic Theory
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Policy & Global Affairs > Economics
SWORD Depositor:
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