This paper examines the daily return series of four main indices, including Shanghai Stock Exchange Composite Index (SSE), Shenzhen Stock Exchange Component Index (SZSE), Shanghai Shenzhen 300 Index (SHSE-SZSE300), and CSI Smallcap 500 index (CSI500) in Chinese stock market from 2000 to 2018 by multifractal detrended fluctuation analysis (MF-DFA). The series of the daily return of the indices exhibit significant multifractal properties on the whole time scale and SZSE has the highest multifractal properties among the four indices, indicating the lowest market efficiency. The multifractal properties of four indices are due to long-range correlation and fat-tail characteristics of the non-Gaussian probability density function, and these two factors have different effects on the multifractality of four indices. This paper aims to compare the multifractility degrees of the four indices in three sub-samples divided by the 2015 stock market crash and to discuss its effects on efficiency of the Shanghai and Shenzhen stock market in each sub-sample. Meanwhile, we study the effect of the 2015 stock market crash on market efficiency from the statistical and fractal perspectives, which has theoretical and practical significance in the application of Effective Market Hypothesis (EMH) in China’s stock market, and it thereby affects the healthy and sustainability of the market. The results also provide important implications for further study on the dynamic mechanism and efficiency in stock market and they are relevant to portfolio managers and policy makers in a number of ways to maintain the sustainable development of China’s capital market and economy.

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This study investigates the efficiencies of the exchange markets for four major currencies-the euro (EUR), the pound (GBP), the Canadian dollar (CAD) and the Japanese yen (JPY)-from 2005 to 2019 by using multifractal detrended fluctuation analysis (MF-DFA). This study also investigates the causes of these efficiencies. Significant multifractal properties are demonstrated by the four markets, and long-range correlation and fat-tail distribution properties are the main causes. We calculate and compare the multifractal degrees in three subsamples, which are classified based on their temporal relation to two economic events: the 2008 financial crisis and the announcement by the Federal Reserve of its withdrawal from the quantitative easing policy in 2014. Empirical results suggest that multifractal properties exist at different levels in the subsamples, thus showing that these events affect foreign exchange market efficiencies in terms of statistics and the fractal market. The JPY exchange market has the fewest multifractal properties, thus indicating that this exchange market has the highest market efficiency among these four exchange markets. The empirical results have implications for the nonlinear mechanism and efficiency in foreign exchange markets, which may help investors effectively manage market risks and benefit a stable global economy.

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