The Predictive Power Of Singular Value Decomposition Entropy For Stock Index

As we know,the stock market plays an important role in national economy.Stock index is an important indicator of stock operation,viewed as the stock market "barometer",which policy maker and investor pay more attention.Based on recently research,in the world there are no absolutely efficient market or inefficient market,and the difference about a market is the degree of effectiveness.In other words,any stock market is a condition between efficient and inefficient.so all stock markets are complex dynamic systems.It is beneficial to understanding the rules of stock market operation to use the nonlinear method to research the complex chracteristics and changes of stock market.Entroy is a kind of measurement of the uncertainty of system state as well as an index reflecting the complex degree of signals.It means the more complex signal which contains more abundant information if the value of entropy is larger.As a nonlinear complex indicator,the research about the predictive power for the stock market of entroy create a new views to analyse market efficience.This paper analyse the singular value decomposition entropy based on the reconstructed phase space matrix of stock index price series,and the predictive power of which for stock index of 37 global stock markets.The main research works are included as following:(1)This paper select the daily closing price of 37 stock markets,including 23 developed markets and 14 stock markets as the research object.By means of a sliding window,the trajectory matrix of reconstructed attractor with 5 embedding dimension can be created,and through the singular value decomposition we get the Shannon entropy,and then we can get 37 singular value decomposition entropy series.(2)Using the linear Granger causality test(traditional Granger causality test,Granger causality test base onVEC model and T-Y Granger causality)and nonlinear Granger causality test(include BDS nonlinear test)to anaylse the relation of singular value decomposition entropy series and stock index.Trough research mentioned above,we found that through nonlinear Granger causality,the entropy series of all the stock markets have the predictive power for stock index,the result is better than linear Granger causality test;the entropy of both developed markets and emerging markets have the predictive power for stock index,it means that the predictive ability of the singular value decomposition entropy based on the reconstructed phase space matrix of price series is not related to the mature degree of stock market.