Asymmetric market efficiency using the index-based asymmetric-MFDFA

We explore the asymmetric market efficiency for various countries' stock indices using the index-based asymmetric-MFDFA. We divide market based on its trend within certain sub-period. Then, we test whether the overall, up-, and down-trend markets are efficient via the asymmetric generalized Hurst exponent. At first, we provide the criteria for testing the asymmetric market efficiency based on the Monte Carlo simulation using the Brownian motion. Secondly, we analyze the asymmetric market efficiency of 34 countries for different sub-periods by comparing the Hurst exponents of original and shuffled time series. We discover that the sources of inefficiency are different with respect to time periods by presenting the groups of countries based on the asymmetric market inefficiency. Lastly, we discuss a time-varying feature of market efficiency where the wider gap between the up- and down-trend efficiency and the stronger correlation between stock index and the asymmetric Hurst exponent are discovered during the financial crisis.