High-dimensional delay selection for regression models with mutual information and distance-to-diagonal criteria

Delay selection for time series phase space reconstruction may be performed using a mutual information (MI) criterion. However, the delay selection is in that case limited to the estimation of a single delay using MI between two variables only. A high-dimensional estimator of the MI may be used to select more than one delay between more than two variables but this approach is rather time consuming. In this paper, an alternative fast criterion is proposed to optimize all delays for a high-dimensional phase space reconstruction: the distance-to-diagonal (DD) criterion, based on a geometrical heuristic. The use of the distance to diagonal criterion is illustrated and compared to MI on artificial and benchmark time series.