This paper examines the stock market comovements using basically three different approaches. Firstly, we used the most common linear analysis, based on cointegrationand Granger causality tests ; secondly we applied a nonlinear approach, using mutual information to analyze nonlinear dependence. Since underlying data sets are affected by non-stationarities  , we also applied MF-DFA and MF-DXA in order to examine the multifractality nature of data and to analyze the relationship and mutual interaction between pairs of series, respectively. The overall results are quite interesting, since we found only 170 pair of stock markets cointegrated, and according to the Granger causality and mutual information we realized that the strongest relations lies between emerging markets, and between emerging and frontier markets. According to scaling exponent given by MF-DFA , h(q=2)>1, we found that all underlying data  belong to non-stationary process. There is no cross-over in the fluctuation functions determined by MF-DFA method confirmed that mentioned approach could remove trends embedded in the data sets\pm0\pm  . The nature of cross-correlation exponent based on Mf-DXA is almost multifractal for all stock market pairs . The empirical relation, h_{xy}\le [ h_{xx + h_{yy ]/2 was confirmedjust for q>0 , while for q<0 there was a deviation from this relation . Width of singularity spectrum is in the range \Delta \alpha_{xx}\in [0.304,0.905] which is another confirmation about multifractality nature of underlying data sets. The singularity spectrum for cross-correlation is in the range \Delta \alpha_{xy}\in [0.246,1.178] confirming more complex relation between stock markets . The value of \sigma_{DCCA} which is a measure for quantifying degree of cross-correlation indicates that all stock market pairs in the underlying time interval belong to cross-correlated series .
Stock market comovements are examined using cointegration, Granger causality tests and nonlinear approaches in context of mutual information and correlations. Underlying data sets are affected by non-stationarities and trends , we also apply AMF-DFA and 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 EMH, only 8 markets are classified in uncorrelated processes at 2\sigma 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\pm0.004 and Jordan with H=0.602\pm 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, H_{xy}\le [ H_{xx + H_{yy ]/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 and global conditions. Width of singularity spectrum for auto-correlation and cross-correlation are \Delta \alpha_{xx}\in [0.304,0.905] and \Delta \alpha_{xy}\in [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 \sigma_{DCCA} indicates that all pairs of stock market studied in this time interval belong to cross-correlated processes .
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