Maksim Kornilov

External low-frequency interference (including interference with a pronounced main frequency) is a common problem in measurements of complex signals, which can affect results of coupling estimation. Since it is impossible to completely remove the interference without affecting the signal itself, the question arises: what distorts the results of coupling estimation to a lesser extent: filtering the interference or ignoring it?
The Granger causality (GC) method is one of the most popular approaches to the detection of directional coupling from observed signals. GC uses predictive empirical models, mostly, linear and nonlinear autoregressive models (recurrence maps). Since the method is highly parametric, its success depends primarily on the parameters of the models and on the properties of the signals. Therefore, the method has to be adapted to the data. In physiology and climatology, most signals have a pronounced time scale, so one of the most important problems is that of adapting the Granger causality method to signals with a selected time scale.
The purpose of this paper is to formulate recommendations for using the Granger causality method for signals with a pronounced temporal scale in the presence of common low-frequency interference. In this paper, we restrict our attention to the case of testing for unilateral coupling and use the recommendations and criteria, developed earlier, for the effectiveness of the method. The sensitivity and specificity of the method are estimated based on surrogate time series. The testing is performed using reference systems of nonlinear dynamics and radiophysics.
It is shown that the loss of sensitivity and specificity of the method decrease nonlinearly with increasing amplitude of the total interference. This dependence varies for different parameters of the method. If the power of interference is several per cent of the signal power, the best results can be achieved by an appropriate choice of parameters of the method rather than by filtering the interference. At a higher noise power, filtering is preferable.

The detection of coupling presence and direction between various systems using their time series is a common task in many areas of knowledge. One of the approaches used to solve it is nonlinear Granger causality method. It is based on the construction of forecasting models, so its efficiency defends on selection of model parameters. Two parameters are important for modeling signals with a main time scales: lag that is used for state vector reconstruction and prediction length.
In this paper, we propose two criteria for evaluating performance of the method of nonlinear Granger causality. These criteria allow to select lag and prediction length, that provide the best sensitivity and specificity. Sensitivity determines the weakest coupling method can detect, and specificity refers to the ability to avoid false positive results. As a result of the criteria application to several etalon unidirectionally coupled systems, practical recommendations for the selection of the model parameters (lag and prediction length) were formulated.