A methodology for detection of causal relationships between discrete time series on systems

Abstract

The need for detecting causality relations of process, events or variables is present in many areas of knowledge, e.g., distributed computing, the stock market, industry and medical sector. This occurs because the knowledge of these relations can often be helpful in solving a variety of problems. For example, maintaining the consistency of replicated databases when writing distributed algorithms or optimizing the purchase and sale of stocks in the stock market. In this context, this dissertation proposes a new methodology for detecting causality relations in systems by using information criteria and Bayesian networks to generate the most probable structure of connections between discrete time series. Modeling the system as a directed graph, in which the nodes are the discrete time series and the edges represent the relations, the main idea of this work is to detect causality relations between the nodes. This detection is made using the method of transfer entropy, which is a method to quantify the information transferred between two variables, and the K2 algorithm: a heuristic method whose objective is to find the most probable belief-network structure, given a data set. Because K2 depends on the premise of having a previous structure that defines the hierarchy among the network nodes, it is proposed in the methodology the creation of the previous ordering on the nodes considering direct and indirect relations, and the modeling of these relations according to the lag between cause and effect. In addition, knowing that the K2 algorithm considers that each case of the data set occurs simultaneously, the proposed methodology modifies the original algorithm by inserting the dynamics of these lags into it. This modification provides a mechanism for comparing direct and indirect causality relations regarding its contribution to the structure. As the result, it is obtained a graph of causality relations between the series, with the relation’s lags being explicit.