Behaviour of Granger causality under filtering: theoretical invariance and practical application

Area of Science:

• Neuroscience
• Signal Processing
• Time Series Analysis

Background:

• Granger causality (G-causality) is widely used for inferring directed functional connectivity in neural time series.
• The impact of common preprocessing techniques, like filtering, on G-causality is not well understood.
• Filtering is typically applied to remove artifacts or focus on specific frequency bands.

Purpose of the Study:

• To investigate the effect of filtering on Granger causality inference in neural time series.
• To determine if filtering can isolate frequency-specific G-causal relationships.
• To propose and evaluate alternatives for frequency-specific G-causality analysis.

Main Methods:

• Theoretical analysis of Granger causality for stationary vector autoregressive (VAR) processes under invertible filtering.
• Development and illustration of band-limited G-causality by integrating spectral G-causality.
• Empirical evaluation using a minimal analytically solvable model to assess changes in G-causality after filtering.
• Demonstration of filtering for removing nonstationary noise components.

Main Results:

• Granger causality is theoretically invariant under arbitrary invertible filtering for stationary VAR processes.
• Filtering does not isolate frequency-specific G-causal inferences.
• Empirical filtering can alter G-causality results due to increased model order.
• Band-limited G-causality provides a valid approach for frequency-specific causal analysis.
• Filtering is effective for removing nonstationary artifacts like line noise.

Conclusions:

• Filtering is inappropriate for isolating causal influences within specific frequency bands.
• While filtering can aid in artifact removal and improve stationarity, it does not enable frequency-specific G-causality.
• Band-limited G-causality is a recommended method for frequency-specific causal inference in neural data.