Causality in time series: dynamic time warping versus granger causality

Causality is a concept studied in various areas such as economics, and engineering. Identifying the cause and effect relations among variables is important as it enables the control of the effected variable by the variation of the cause or helps predict the future behavior of the effected variable based on the behavior of the cause. Granger Causality (GC) test is a statistical test mainly used for causality detection in economics and recently in bioinformatics. The GC test determines whether one series Granger causes the other or not, or if there exists a feedback relation. However, results of the GC tests do not elucidate how these relations change with time. Dynamic Time Warping (DTW) is a method employed for similarity measurement in classification and clustering applications, in areas such as speech recognition and batch trajectory synchronization. In the DTW method, principles of dynamic programing are utilized and the series are aligned nonlinearly in the time axis. In this thesis work, it is proposed that DTW can help determine the temporal order and the lead/lag relations of the series, therefore, the causal relations. The DTW method is tested on selected synthetic data sets and on data from chemical and biochemical processes, and engineering related economic indicators. The DTW-based causality results are compared with those of the GC tests and cross-correlation analyses. The DTW-based results were found to be as expected and in accordance with the GC test only for the simple examples, for multivariable sets and nonlinearly-related variables, the method was unsuccessful.