CAUSALITY IN TIME SERIES FOR MULTIVARIATE DATA

Abstract

In this thesis, we investigate the behavior of conditional correlations among major cryptocurrencies. Our findings suggest that correlations between cryptocurrencies are positive, but vary over time. However, determining the direction of causality and the presence of feedback between related variables can be challenging in some cases. To address this, we propose testable definitions of causality and feedback and demonstrate their use in simple two-variable models. We also address the problem of apparent instantaneous causality, which can arise due to delays in recording information or inadequate consideration of possible causal variables. We show that the cross spectrum between two variables can be separated into two parts, each representing a single causal arm in a feedback situation. Using this approach, we can develop measures of causal lag and strength. Finally, we suggest a generalization of these results with the partial cross spectrum.