A model order selection criterion with applications to cardio-respiratory-renal systems

We introduce a model order selection criterion called signal prediction error (SPE) for the identification of a linear regression model, which can be an adequate representation of a resting physiologic system. SPE is an estimate of the prediction error variance due only to model estimation error and not unobserved noise, which distinguishes it from the widely used final prediction error (FPE). We then present a theoretical analysis of SPE, which predicts that its ability to select correctly the model order is more dependent on the signal-to-noise ratio (SNR) and less dependent on the number of data samples available for analysis. We next propose a heuristic procedure based on SPE (called SPE(D)) to improve its robustness to SNR levels. We then demonstrate, through simulated physiologic data at high SNR levels, that SPE will be equivalent to consistent model order selection criteria for long data records but will become superior to FPE and other model order selection criteria as the size of the data record decreases. The simulated data results also show that SPE(D) is indeed a significant improvement over SPE in terms of robustness to SNR. Finally, we demonstrate the applicability of SPE and SPE(D) to actual cardio-respiratory-renal data.