Pearson correlation and transfer entropy in the Chinese stock market with time delay

Correlations between two time series, including the linear Pearson correlation and the nonlinear transfer entropy, have attracted significant attention. In this work, we studied the correlations between multiple stock data with the introduction of a time delay and a rolling window. In most cases, the Pearson correlation and transfer entropy share the same tendency, where a higher correlation provides more information for predicting future trends from one stock to another, but a lower correlation provides less. Considering the computational complexity of the transfer entropy and the simplicity of the Pearson correlation, using the linear correlation with time delays and a rolling window is a robust and simple method to quantify the mutual information between stocks. Predictions made by the long short-term memory method with mutual information outperform those made only with self-information when there are high correlations between two stocks.