Jensen-Detrended Cross-Correlation function for non-stationary time series with application to Latin American stock markets

Variance has an important role in statistics and information theory fields, by forming the basis for many well-known information measures. Based on Jensen's inequality and variance, the Jensen-variance information has been previously proposed to measure the distance between two random variables. Jensen-variance distance is based on the convexity property of random variable variance. Based on the relationship between Jensen-variance distance and classical Detrended Cross-Correlation (DCC) of two not necessarily stationary process, the Jensen-Detrended Covariance and Jensen-DCC functions are proposed in this paper. Moreover, Jensen-DCC function is also considered for Hénon and Logistic chaotic maps for simulated time series. Then we considered a stock market time series dataset for the study of similarity of Latin American indexes with S&P500 and Shanghai ones. We obtained a useful tool to study the similarity or distance of two non-stationary time series based on DCC coefficient.