Causality in Time Series Systems

Abstract

Causality inference for time series systems has been subject to intensive research across many generations of physicist and, in light of the boom of computational resources, has been increasingly applied to a wider range of areas such as biology or finance. In this thesis we structurally compare three inference methods, Granger Causality, Transfer Entropy, and Convergent Cross Mapping, by applying them to synthetic nonlinear systems. While we verify that Granger Causality only detects linear causal relations, our analysis with Fourier Transform surrogates shows that a significant amount of causality, measured by Transfer Entropy and Convergent Cross Mapping, is driven by nonlinear properties. Our study of the Lorenz attractor further suggests different structures for different timeframe lengths. Upon introducing measures for the system causality, we observe that the long-term causality of the system remains approximately constant with a major nonlinear component. On a short-term scale, the causality resolution changes, which we can map to certain locations within the attractor. We find these properties to apply to several other synthetic nonlinear systems. The resulting framework is designed to be applicable to real-world time series systems in order to detect unknown causality structures and drivers in other research areas.