Using Rényi parameter to improve the predictive power of singular value decomposition entropy on stock market

• Generalized singular value decomposition entropy is proposed.
• The meaning of different qq in our method has been explored.
• Its predictive power has been examined in the stock market.
• Noises and errors affect SCI more frequently than DJI.

This paper generalizes the method of traditional singular value decomposition entropy by incorporating orders qq of Rényi entropy. We analyze the predictive power of the entropy based on trajectory matrix using Shanghai Composite Index and Dow Jones Index data in both static test and dynamic test. In the static test on SCI, results of global granger causality tests all turn out to be significant regardless of orders selected. But this entropy fails to show much predictability in American stock market. In the dynamic test, we find that the predictive power can be significantly improved in SCI by our generalized method but not in DJI. This suggests that noises and errors affect SCI more frequently than DJI. In the end, results obtained using different length of sliding window also corroborate this finding.