Detection of Causal Relationships Based on Residual Analysis

The detection of causal interactions between variables from time series data is an important problem in many research areas. Granger causality is a well-known approach that uses prediction error to infer causality. However, the autoregressive models fitted to data usually do not pass model validation tests based on residual analysis, resulting in low causality values that can be inconclusive. The method proposed here fits models for paired combination of all variables and inferences about causality are provided after performing residual analysis. The model order is increased until the autocorrelation test of residual and cross-correlation test of residuals and input provide an answer about causality. The thresholds to decide the existence of causality are provided directly by the data. Higher order multivariate systems are similarly considered and a test to check if causality is direct or indirect is also proposed. The utility of the proposed approach is illustrated by several examples including application on a simulated data set and routine operating data from industry for causality analysis.