Time series classification based on detrended partial cross-correlation

Classifying stocks by measuring the similarity between them can provide investors with a reliable reference and help them earn more profits than before. This paper attempts to explore a convincing method to measure the similarity of international stocks. We selected the daily closing prices of 18 stocks from the Americas, Asia, Europe, and Australia, and mapped them as points into a three-dimensional space. In order to measure the similarity of stocks, we recommend calculating the Hurst surface distance as a distance matrix to classify stocks through the multidimensional scaling (MDS) method. We compare the classification results with classical MDS using Euclidean distance as similarity measure and MDS based on the $\rho_{D P X A}$ (the detrending partial cross-correlation (DPXA) coefficient). The research results show that using Hurst surface distance as a reflection of similarity can not only provide more relevant information, but also distinguish the differences of economic fluctuations in different regions, while $\rho_{D P X A}$ lays more emphasis on the similarities and differences within the same region. Both the two improved techniques for MDS are superior to the classic method based on Euclidean distance. In addition, the two methods can provide more detailed and clearer information