Causal Inference On Time Series Using Causal Strength

With the rapid development of information technology, lots of time series data is collected in business and science.Time series is a statistical indicator of a certain phenomenon(such as temperature, stock index, pulse, etc.) at different time in chronological order.Compared with traditional static data, time series contains unknown and valuable rules and mechanisms related to temporal dynamics,therefore, if we can dig out the knowledge of data and predict or intervente the trends of time series,there will be very important for scientific research, business marketing, engineering production and so on.The objective of this paper is to infer the causal network behind time series data. Because there will always be causality between different time series, and the causal network is an effective tool for the analysis of causality between things,therefore,causal network is more suitable for research time series than other methods,and it has become a common method in this field. The essence of causal network inference is selecting strong relationship between nodes to construct a complete causality graph,because the strength of the causal relationship between different nodes are different,an accurately measure of causality strength is badly need. However,traditional measure will result in many redundancies, and its dimension isn’t uniform,which means it can’t measure the strength accurately, and seriously affect the accuracy of the inference.To solve this problem, the work of this paper can be divided into two parts:First, we try to solve the two problem aroused by traditional measure of causality strength,this paper propose a new measure of causality strength based on information entropy,called’Normalized Causal Entropy", which uses normalization, so it makes strength between nodes with different dimension be comparable, unified strength dimension between nodes with different information, in the meantime,by excluding indirect effects between nodes, it reduce overestimating of strength, significantly reducing redundancy,these two improvements make’Normalized Causal Entropy"a more accurately measure for the causal strength between time series nodes comparing to traditional methods;Second,based on, we design time series causality network inference algorithm,using’Normalized Causal Entropy" as measure of causal strength between nodes, screened "fathers" with strong relationship to a single node, and iterate each node’s corresponding "father" for sub-graph,and finally complete causality diagram.In the experimental part, this paper utilize an artificially generated simulation data set, carried out experiments on Matlab platform.First, we set standard data set,and test the performance of conventional algorithms and "Normalized Causal Entropy" by ROC test,the results show that with same recall,’Normalized Causal Entropy" significantly reduce the FP rate, and performs better in the overall;Second,by changing the characteristic of standard data set,we test the sensitivity to data characteristics of’Normalized Causal Entropy" and traditional methods, The results shows that,’Normalized Causal Entropy" is more robust with data characteristics; Third, according to the results,we analyse the shortages and improvements of’Normalized Causal Entropy".