Nonlinear Dynamic Causality Inference in Time Series

Abstract

The main focus of this work is on detection of causal relationships or couplings between different processes or systems. Identification of these causal relationships has applications in many disciplines including physics, economics, biology, neuroscience, and climatology. As these couplings or causal relationships are inherently hidden in the underlying dynamics of the system and are not necessarily accessible, we develop methods to discover these interactions by some observations of the system measured in the form of a time series. In the first part of our work, we propose a new method called the coupling spectrum (CS) for inference of the directed coupling in a deterministic system. We will observe that this method can identify the direction of coupling in sever conditions such as bidirectional couplings, nonlinear dynamics, nonidentical and multivariate systems, small sample sizes, weak couplings, as well as multi-scale and noisy data. Later, we study a biological and a financial application of the CS method. First, we analyze the microarray data for inference of the gene regulatory networks, one of the most important biological networks that their identification has immediate applications in cancer prediction. Then, the CS method is used for detection of the temporal causality between the stock prices of two companies. The analysis of empirical data in these applications show the successful performance of the CS method in real-world problems. In the last part of our contributions, we propose a new method for inference of the distributional causality, a kind of causality that its inference has applications in finance and econometrics. Our method provides information about the influence of the causality on the underlying distribution of the processes. The analysis of the simulated and empirical financial data shows the success of our method.