  This study investigates empirically whether the degree of stock market
efficiency is related to the prediction power of future price change using the
indices of twenty seven stock markets. Efficiency refers to weak-form efficient
market hypothesis (EMH) in terms of the information of past price changes. The
prediction power corresponds to the hit-rate, which is the rate of the
consistency between the direction of actual price change and that of predicted
one, calculated by the nearest neighbor prediction method (NN method) using the
out-of-sample. In this manuscript, the Hurst exponent and the approximate
entropy (ApEn) are used as the quantitative measurements of the degree of
efficiency. The relationship between the Hurst exponent, reflecting the various
time correlation property, and the ApEn value, reflecting the randomness in the
time series, shows negative correlation. However, the average prediction power
on the direction of future price change has the strongly positive correlation
with the Hurst exponent, and the negative correlation with the ApEn. Therefore,
the market index with less market efficiency has higher prediction power for
future price change than one with higher market efficiency when we analyze the
market using the past price change pattern. Furthermore, we show that the Hurst
exponent, a measurement of the long-term memory property, provides more
significant information in terms of prediction of future price changes than the
ApEn and the NN method.
