The long memory and the transaction cost in financial markets

In the present work, we investigate the fractal dimensions of 30 important stock markets from 2006 to 2013; the analysis indicates that the Hurst exponent of emerging markets shifts significantly away from the standard Brownian motion. We propose a model based on the Hurst exponent to explore the considerable profits from the predictable long-term memory. We take the transaction cost into account to justify why the market inefficiency has not been arbitraged away in the majority of cases. The empirical evidence indicates that the majority of the markets are efficient with a certain transaction cost under the no-arbitrage assumption. Furthermore, we use the Monte Carlo simulation to display “the efficient frontier” of the Hurst exponent with different transaction costs.