  This paper investigates the degree of efficiency for the Moscow Stock
Exchange. A market is called efficient if prices of its assets fully reflect
all available information. We show that the degree of market efficiency is
significantly low for most of the months from 2012 to 2021. We calculate the
degree of market efficiency by (i) filtering out regularities in financial data
and (ii) computing the Shannon entropy of the filtered return time series. We
have developed a simple method for estimating volatility and price staleness in
empirical data, in order to filter out such regularity patterns from return
time series. The resulting financial time series of stocks' returns are then
clustered into different groups according to some entropy measures. In
particular, we use the Kullback-Leibler distance and a novel entropy metric
capturing the co-movements between pairs of stocks. By using Monte Carlo
simulations, we are then able to identify the time periods of market
inefficiency for a group of 18 stocks. The inefficiency of the Moscow Stock
Exchange that we have detected is a signal of the possibility of devising
profitable strategies, net of transaction costs. The deviation from the
efficient behavior for a stock strongly depends on the industrial sector it
belongs.
