A New Distance Correlation Metric and Bagging Method for NARX Model Estimation

System identification is a challenging and interesting engineering problem that has been studied for decades. In particular, the NARMAX methodology has been extensively used with interesting results. Such methodology identifies a deterministic parsimonious model by ranking a set of candidate terms using a linear dependency metric with respect to the output. Other metrics have been used that identify nonlinear dependencies, like the mutual information, but they are hard to interpret. In this work, the distance correlation metric is implemented together with the bagging method. These two implementations enhance the performance of the NARMAX methodology providing interpretability of nonlinear dependencies and uncertainty measures in the model identified. A comparison of the new BOFR-dCor (Bagging Orthogonal Forward Regression using distance Correlation) algorithm is done with respect to the traditional OFR (Orthogonal Forward Regression) algorithm and the OFR-MI (Orthogonal Forward Regression using Mutual Information) algorithm showing interesting results that improve interpretability and uncertainty analysis.