Evaluation of the autoregression time-series model for analysis of a noisy signal

Abstract

The autoregression (AR) time-series model of a continuous noisy signal was statistically evaluated to determine quantitatively the uncertainties of the model order, the model parameters, and the model's power spectral density (PSD). The result of such a statistical evaluation enables an experimenter to decide whether an AR model can adequately represent a continuous noisy signal and be consistent with the signal's frequency spectrum, and whether it can be used for on-line monitoring. Although evaluations of other types of signals have been reported in the literature, the author has found no direct reference to AR model's uncertainties for continuous noisy signals; yet the evaluation is necessary to decide the usefulness of AR models of typical reactor signals (e.g., neutron detector output or thermocouple output) and the potential of AR models for on-line monitoring applications. AR and other time-series models for noisy data representation are being investigated by others since such models require fewer parameters than the traditional PSD model (1 to 4). For this study, the AR model was selected for its simplicity and conduciveness to uncertainty analysis, and controlled laboratory bench signals were used for continuous noisy data.