Time-Frequency Causal Inference Uncovers Anomalous Events in Environmental Systems
Causal inference in dynamical systems is a challenge for different research areas. So far it is mostly about understanding to what extent the underlying causal mechanisms can be derived from observed time series. Here we investigate whether anomalous events can also be identified based on the observed changes in causal relationships. We use a parametric time-frequency representation of vector autoregressive Granger causality for causal inference. The use of time-frequency approach allows for dealing with the nonstationarity of the time series as well as for defining the time scale on which changes occur. We present two representative examples in environmental systems: land-atmosphere ecosystem and marine climate. We show that an anomalous event can be identified as the event where the causal intensities differ according to a distance measure from the average causal intensities. The driver of the anomalous event can then be identified based on the analysis of changes in the causal effect relationships.
KeywordsTime-frequency causality analysis Vector Autoregressive Granger Causality Attribution of anomalous events
The authors thank the Carl Zeiss Foundation for the financial support within the scope of the program line “Breakthroughs: Exploring Intelligent Systems” for “Digitization—explore the basics, use applications”. This work used eddy covariance data acquired and shared by the FLUXNET community.
- 2.Wan, E.A., Nelson, A.T.: Dual Extended Kalman Filter Methods, pp. 123–173. Wiley-Blackwell (2002). https://doi.org/10.1002/0471221546.ch5. Chapter 5
- 6.Baccalá, L.A., Sameshima, K., Takahashi, D.: Generalized partial directed coherence. In: 15th International Conference on Digital Signal Processing, pp. 163–166. IEEE (2007)Google Scholar
- 8.Barz, B., Guanche, Y., Rodner, E., Denzler, J.: Maximally divergent intervals for extreme weather event detection. In: MTS/IEEE OCEANS Conference Aberdeen, pp. 1–9 (2017). https://doi.org/10.1109/OCEANSE.2017.8084569
- 23.Reichstein, M., Camps-Valls, G., Stevens, B., Jung, M., Denzler, J., Carvalhais, N., Prabhat: Deep learning and process understanding for data-driven earth system science. Nature 195–204 (2019). https://doi.org/10.1038/s41586-019-0912-1
- 26.Shadaydeh, M., Garcia, Y.G., Mahecha, M., Reichstein, M., Denzler, J.: Causality analysis of ecological time series: a time-frequency approach. In: Chen, C., Cooley, D., Runge, J., Szekely, E. (eds.) Climate Informatics Workshop 2018, pp. 111–114 (2018)Google Scholar
- 30.Trifunov, V.T., Shadaydeh, M., Runge, J., Eyring, V., Reichstein, M., Denzler, J.: Nonlinear causal link estimation under hidden confounding with an application to time series anomaly detection. In: German Conference on Pattern Recognition (2019)Google Scholar