Due to the strong complexity of financial markets, economics does not have a unified theory of price formation in financial markets. The most common assumption is the Efficient-Market Hypothesis, which has been attacked by a number of researchers, using different tools. There were varying degrees to which these tools complied with the formal definitions of efficiency and predictability. In our earlier work, we analysed the predictability of stock returns at two time scales using the entropy rate, which can be directly linked to the mathematical definition of predictability. Nonetheless, none of the above-mentioned studies allow any general understanding of how the financial markets work, beyond disproving the Efficient-Market Hypothesis. In our previous study, we proposed the Maximum Entropy Production Principle, which uses the entropy rate to create a general principle underlying the price formation processes. Both of these studies show that the predictability of price changes is higher at the transaction level intraday scale than the scale of daily returns, but ignore all scales in between. In this study we extend these ideas using the multiscale entropy analysis framework to enhance our understanding of the predictability of price formation processes at various time scales.
predictability market efficiency information theory