Quantum mechanics

Autocorrelation

Determinism

Biology

Statistics

Causal inference

Multivariate statistics

Time series

Curse of dimensionality

Data mining

Computer science

Filter (signal processing)

Paleontology

Physics

Mathematics

Image (mathematics)

Sampling (signal processing)

Econometrics

Artificial intelligence

Series (stratigraphy)

Noise (video)

Causality (physics)

Machine learning

Computer vision

Chaos An Interdisciplinary Journal of Nonlinear Science

Causal network reconstruction from time series is an emerging topic in many fields of science. Beyond inferring directionality between two time series, the goal of causal network reconstruction or causal discovery is to distinguish direct from indirect dependencies and common drivers among multiple time series. Here, the problem of inferring causal networks including time lags from multivariate time series is recapitulated from the underlying causal assumptions to practical estimation problems. Each aspect is illustrated with simple examples including unobserved variables, sampling issues, determinism, stationarity, nonlinearity, measurement error, and significance testing. The effects of dynamical noise, autocorrelation, and high dimensionality are highlighted in comparison studies of common causal reconstruction methods. Finally, method performance evaluation approaches and criteria are suggested. The article is intended to briefly review and accessibly illustrate the foundations and practical problems of time series-based causal discovery and stimulate further methodological developments.

Causal network reconstruction from time series: From theoretical assumptions to practical estimation