Tests for partial correlation between repeatedly observed nonstationary nonlinear timeseries

TL;DR

This paper introduces two statistical tests for detecting partial correlation in nonstationary, nonlinear timeseries, applicable to multiple independent recordings without assuming stationarity or linearity.

Contribution

The paper presents novel nonparametric tests for partial correlation in complex timeseries, accommodating nonstationarity and nonlinearity, using multiple independent recordings.

Findings

Tests effectively detect partial correlation in complex timeseries.

No assumptions of stationarity or linearity are required.

Applicable to multiple independent recordings.

Abstract

We describe two families of statistical tests to detect partial correlation in vectorial timeseries. The tests measure whether an observed timeseries Y can be predicted from a second series X, even after accounting for a third series Z which may correlate with X. They do not make any assumptions on the nature of these timeseries, such as stationarity or linearity, but they do require that multiple statistically independent recordings of the 3 series are available. Intuitively, the tests work by asking if the series Y recorded on one experiment can be better predicted from X recorded on the same experiment than on a different experiment, after accounting for the prediction from Z recorded on both experiments.