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The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable. [ABSTRACT FROM AUTHOR]