Eberlein, Robert L. with Qifan Wang, "Validation of Oscillatory Behavior Modes Using Spectral Analysis", 1983
ua435
In this paper we outline and evaluate a simple technique for analyzing the ability of a model to reproduce an oscillatory behavior mode. The technique consists of using a model as a predictor, and then performing spectral analysis on the prediction errors. The technique is referred to as the spectral analysis of residuals or SAR test. The paper motivates the use of prediction residuals and illustrates the technique with a simple model of inventory oscillation. The SAR test appears to yield a substantial amount of information about the performance of a model. However, the technique breaks down if the observed behavior is a result of the system being subjected to shocks with similar dynamic characteristics to the system output or if the system has more than one set of mechanisms generating the behavior of interest. The SAR test is not capable of distinguishing between models which can explain the behavior equally well using different state space representations.