Assessment of 48 Stock markets using adaptive multifractal approach

In this paper, Stock market comovements are examined using cointegration, Granger causality tests and nonlinear approaches in context of mutual information and correlations. Since underlying data sets are affected by non-stationarities and trends, we also apply Adaptive Multifractal Detrended Fluctuation Analysis (AMF-DFA) and Adaptive Multifractal Detrended Cross-Correlation Analysis (AMF-DXA). We find only 170 pair of Stock markets cointegrated, and according to the Granger causality and mutual information, we realize that the strongest relations lies between emerging markets, and between emerging and frontier markets. According to scaling exponent given by AMF-DFA, h(q=2)>1, we find that all underlying data sets belong to non-stationary process. According to Efficient Market Hypothesis (EMH), only 8 markets are classified in uncorrelated processes at 2σ confidence interval. 6 Stock markets belong to anti-correlated class and dominant part of markets has memory in corresponding daily index prices during January 1995 to February 2014. New-Zealand with H=0.457±0.004 and Jordan with H=0.602±0.006 are far from EMH. The nature of cross-correlation exponents based on AMF-DXA is almost multifractal for all pair of Stock markets. The empirical relation, Hxy≤[Hxx+Hyy]∕2, is confirmed. Mentioned relation for q>0 is also satisfied while for q<0 there is a deviation from this relation confirming behavior of markets for small fluctuations is affected by contribution of major pair. For larger fluctuations, the cross-correlation contains information from both local (internal) and global (external) conditions. Width of singularity spectrum for auto-correlation and cross-correlation are Δαxx∈[0.304,0.905] and Δαxy∈[0.246,1.178], respectively. The wide range of singularity spectrum for cross-correlation confirms that the bilateral relation between Stock markets is more complex. The value of σDCCA indicates that all pairs of stock market studied in this time interval belong to cross-correlated processes.