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Area of Science:

  • Time Series Analysis
  • Causality Detection
  • Stochastic Processes

Background:

  • The directionality of information flow in time series is crucial for understanding complex systems.
  • Standard Granger causality (GC) analysis often assumes normal distribution of errors, limiting its applicability.
  • Investigating time-reversed series offers potential for more robust causality detection.

Purpose of the Study:

  • To investigate the information flow time arrow for stochastic data using vector autoregressive models.
  • To evaluate the performance of Granger causality tests and time-reversal methods under various error distributions.
  • To identify conditions under which standard GC may fail and how backward analysis can improve accuracy.

Main Methods:

  • Analysis of time series data using vector autoregressive models.
  • Application of standard Granger causality (GC) tests on original and time-reversed series.
  • Utilizing methods based on time reversal testing for causality detection.
  • Consideration of various predictive error distributions beyond the normal distribution.

Main Results:

  • Standard GC detected bidirectional causal connections under specific conditions related to connection strength and predictive error ratios.
  • Time-reversal testing methods unconditionally detected opposite causal links but struggled with accurate bidirectional detection.
  • A clear effect of changing cause-effect order was detected on time-reversed series for unidirectionally connected variables.

Conclusions:

  • Backward analysis is valuable for rejecting falsely detected unidirectional connections by comparing with time-reversed results.
  • Time-reversal methods can confirm the absence of causal links in uncorrelated, causally independent variables.
  • The study highlights limitations of standard GC and the utility of time-reversed analysis for accurate causality assessment.