  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-minute and 5-minute price time series
of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a
methodology to isolate true 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.
