Based on the China Securities Index 300 (CSI 300 index) futures trading restrictions in 2015, this paper uses the multifractal detrending moving-average cross-correlation analysis method (MF-X-DMA) to investigate the effect of introducing futures trading restrictions on the market efficiency of CSI 300 index spot and futures markets. We begin by using multifractal detrending moving-average analysis (MF-DMA) and find that the futures trading restrictions improve spot market efficiency but decrease futures market efficiency. Moreover, we examine the cross-correlation between spot and futures markets and the information transmission process. MF-X-DMA analysis shows an increase in the level of persistent cross-correlation between spot and futures markets, and a decrease in the multifractality degree of cross-correlation, suggesting that the relationship between spot and futures markets becomes stronger and less complicated after the futures trading restrictions. Moreover, the nonlinear Granger causality test shows that futures returns do not Granger cause spot returns after the restrictions. Therefore, the futures trading restrictions may mitigate the harmful effect of speculative trading in the futures market and thus improve spot market efficiency.

Considering that multifractal characteristics widely exists in financial markets, this paper adopts the multifractal detrended cross-correlation analysis (MF-DCCA) method to study the correlation between futures and spot returns in China's soybean market. Based on the data of soybean No. 1 futures and soybean spot price from January 4, 2011 to February 23, 2022, this paper shows that there is a high degree of multifractal cross-correlation between soybean futures and spot returns. Furthermore, this paper proves that the cross-correlation between the two time series are persistent.