Exploratory Causal Analysis in Bivariate Time Series Data Abstract Many scientific disciplines rely on observational data of systems for which it is difficult (or impossible) to implement controlled experiments and data analysis techniques are required for identifying causal information and relationships directly from observational data. This need has lead to the development of many different time series causality approaches and tools including transfer entropy, convergent cross-mapping (CCM), and Granger causality statistics. A practicing analyst can explore the literature to find many proposals for identifying drivers and causal connections in times series data sets, but little research exists of how these tools compare to each other in practice. This work introduces and defines exploratory causal analysis (ECA) to address this issue. The motivation is to provide a framework for exploring potential causal structures in time series data sets. J. M. McCracken Defense talk for PhD in Physics, Department of Physics and Astronomy 10:00 AM November 20, 2015; Exploratory Hall, 3301 Advisor: Dr. Robert Weigel; Committee: Dr. Paul So, Dr. Tim Sauer J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 1 / 50 Exploratory Causal Analysis in Bivariate Time Series Data J. M. McCracken Department of Physics and Astronomy George Mason University, Fairfax, VA November 20, 2015 J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 2 / 50 Outline 1. Motivation 2. Causality studies 3. Data causality 4. Exploratory causal analysis 5. Making an ECA summary Transfer entropy difference Granger causality statistic Pairwise asymmetric inference Weighed mean observed leaning Lagged cross-correlation difference 6. Computational tools for the ECA summary 7. Empirical examples Cooling/Heating System Data Snowfall Data 8. Times series causality as data analysis J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 3 / 50 Question Is there evidence that X \drives" Y? We were looking for a data analysis approach, i.e., we were looking for analysis tools that I worked with time series data, I had straightforward, preferably well-established, interpretations, I were reliable, I and did not require studying the (vast) philosophical causality literature. Essentially, we were looking for a \plug-and-play" analysis tool. This work stems from our search for such a tool. Motivation Data Consider two sets of time series measurements, X and Y. J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 4 / 50 We were looking for a data analysis approach, i.e., we were looking for analysis tools that I worked with time series data, I had straightforward, preferably well-established, interpretations, I were reliable, I and did not require studying the (vast) philosophical causality literature. Essentially, we were looking for a \plug-and-play" analysis tool. This work stems from our search for such a tool. Motivation Data Consider two sets of time series measurements, X and Y. Question Is there evidence that X \drives" Y? J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 4 / 50 I worked with time series data, I had straightforward, preferably well-established, interpretations, I were reliable, I and did not require studying the (vast) philosophical causality literature. Essentially, we were looking for a \plug-and-play" analysis tool. This work stems from our search for such a tool. Motivation Data Consider two sets of time series measurements, X and Y. Question Is there evidence that X \drives" Y? We were looking for a data analysis approach, i.e., we were looking for analysis tools that J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 4 / 50 I had straightforward, preferably well-established, interpretations, I were reliable, I and did not require studying the (vast) philosophical causality literature. Essentially, we were looking for a \plug-and-play" analysis tool. This work stems from our search for such a tool. Motivation Data Consider two sets of time series measurements, X and Y. Question Is there evidence that X \drives" Y? We were looking for a data analysis approach, i.e., we were looking for analysis tools that I worked with time series data, J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 4 / 50 I were reliable, I and did not require studying the (vast) philosophical causality literature. Essentially, we were looking for a \plug-and-play" analysis tool. This work stems from our search for such a tool. Motivation Data Consider two sets of time series measurements, X and Y. Question Is there evidence that X \drives" Y? We were looking for a data analysis approach, i.e., we were looking for analysis tools that I worked with time series data, I had straightforward, preferably well-established, interpretations, J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 4 / 50 I and did not require studying the (vast) philosophical causality literature. Essentially, we were looking for a \plug-and-play" analysis tool. This work stems from our search for such a tool. Motivation Data Consider two sets of time series measurements, X and Y. Question Is there evidence that X \drives" Y? We were looking for a data analysis approach, i.e., we were looking for analysis tools that I worked with time series data, I had straightforward, preferably well-established, interpretations, I were reliable, J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 4 / 50 Essentially, we were looking for a \plug-and-play" analysis tool. This work stems from our search for such a tool. Motivation Data Consider two sets of time series measurements, X and Y. Question Is there evidence that X \drives" Y? We were looking for a data analysis approach, i.e., we were looking for analysis tools that I worked with time series data, I had straightforward, preferably well-established, interpretations, I were reliable, I and did not require studying the (vast) philosophical causality literature. J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 4 / 50 This work stems from our search for such a tool. Motivation Data Consider two sets of time series measurements, X and Y. Question Is there evidence that X \drives" Y? We were looking for a data analysis approach, i.e., we were looking for analysis tools that I worked with time series data, I had straightforward, preferably well-established, interpretations, I were reliable, I and did not require studying the (vast) philosophical causality literature. Essentially, we were looking for a \plug-and-play" analysis tool. J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 4 / 50 Motivation Data Consider two sets of time series measurements, X and Y. Question Is there evidence that X \drives" Y? We were looking for a data analysis approach, i.e., we were looking for analysis tools that I worked with time series data, I had straightforward, preferably well-established, interpretations, I were reliable, I and did not require studying the (vast) philosophical causality literature. Essentially, we were looking for a \plug-and-play" analysis tool. This work stems from our search for such a tool. J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 4 / 50 Causality studies The study of causality is as old as science itself I Modern historians credit Aristotle with both the first theory of causality (\four causes") and an early version of the scientific method I The modern study of causality is broadly interdisciplinary; far too broad to review in a short talk. Illari and Russo's textbook1provides an overview of causality studies 1 Illari, P., & Russo, F. (2014). Causality: Philosophical theory meets scientific practice. Oxford University Press. J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 5 / 50 Foundational causality \Is a cause required to precede an effect?” or \How are causes and effects related in space-time?" Data causality \Does smoking cause lung cancer?" or \Are traffic accidents caused by rain storms?" Towards a taxonomy of causal studies Paul Holland identified four types of causal questions2: I the ultimate meaningfulness of the notion of causality I the details of causal mechanisms I the causes of a given effect I the effects of a given cause 2 Holland, P. W. (1986). Statistics and causal inference. Journal of the American statistical Association, 81(396), 945-960. J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 6 / 50 Data causality \Does smoking cause lung cancer?" or \Are traffic accidents caused by rain storms?" Towards a taxonomy of causal studies Paul Holland identified four types of causal questions2: I the ultimate meaningfulness of the notion of causality I the details of causal mechanisms I the causes of a given effect I the effects of a given cause Foundational causality \Is a cause required to precede an effect?” or \How are causes and effects related in space-time?" 2 Holland, P. W. (1986). Statistics and causal inference. Journal of the American statistical Association, 81(396), 945-960. J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 6 / 50 Towards a taxonomy of causal studies Paul Holland identified four types of causal questions2: I the ultimate meaningfulness of the notion of causality I the details of causal mechanisms I the causes of a given effect I the effects of a given cause Foundational causality \Is a cause required to precede an effect?” or \How are causes and effects related in space-time?" Data