A similarity of multivariate time series in stocks network analysis

Abstract

Correlation-based network as a model for financial markets, especially stock market, is a complex system has received much attention. There have been a lot of studies which deals with stocks network analysis, where each stock is represented by a univariate time series of its closing price, and then the similarity between two stocks are quantified by using Pearson correlation coefficient (PCC) on the logarithmic returns. However, in daily stock market activity, stock is represented by a multivariate time series during its opening, highest, lowest, and closing prices. The solely used of the information from closing price may cause the loss of information from other prices. In this thesis, all four prices are considered. The notion of multivariate time series similarity among stocks are developed. The use of Escoufier vector correlation (EVC), a multivariate generalization of PCC, is proposed to measure the similarity between stocks. Then the EVC coefficients are used to construct the stocks network in multivariate setting based on minimal spanning tree (MST). In the case study on BURSA MALAYSIA, the topological properties of stocks in EVC-based MST and in PCC-based MST are different. The total path lengths among stocks in the economic sector according to EVC-based MST is generally smaller than according to PCC-based MST. It means that with the approach of EVC-based MST, the stocks are strongly connected with other stocks in the same sector. Moreover, EVC is proposed to define the similarity between economic sectors, where each sector is represented by a multivariate time series of p components and each component is a univariate time series of stock’s closing price. To the best of our knowledge, there is no previous studies which deals with the similarity between economic sectors using this approach. The methodology for economic sectors network analysis is formulated in this thesis. The current practice of using Kruskal’s or Prim’s algorithm is to obtain MST, and then sub-dominant ultrametric (SDU) from the MST. It will consume a lot of time when the number of stocks is large. Therefore to solve this problem, an efficient algorithm is developed based on fuzzy relation approach. A comparison study based on the empirical and simulated data shows that the proposed algorithm is faster. The proposed algorithm provides not only MST and SDU, but also the forest of all MSTs.