How to Measure Statistical Causality: A Transfer Entropy Approach with Financial Applications

We’ve all heard the say “correlation does not imply causation”, but how can we quantify causation? This is an extremely difficult and often misleading task, particularly when trying to infer causality from observational data and we cannot perform controlled trials or A/B testing.

Fortunately, we can take advantage of statistics and information theory to uncover complex causal relationships from observational data (remember, this is still a very challenging task).

The objectives of this Article are the following:

  • Introduce a prediction-based definition of causality and its implementation using a vector auto-regression formulation.

  • Introduce a probabilistic-definition of causality and its implementation using an information-theoretical framework.

  • Simulate linear and nonlinear systems and uncover causal links with the proposed methods.

  • Quantify information flow among global equity indexes further uncovering which indexes are driving the global financial markets.

  • Discuss further applications including the impact of social media sentiment in crypto markets.

We also provide code to reproduce results as part of our Open Source Live Book initiative.

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