Optimal selection of parameters of the forecasting models used for the nonlinear Granger causality method in application to the signals with a main time scales

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.