ARMAsel for Detection and Correction of Outliers in Univariate Stochastic Data

Abstract

For stationary random data, an automatic estimation algorithm can now select a time series model with a spectral accuracy close to the Cramér–Rao lower bound. The parameters of that selected time series model accurately represent the spectral density and the autocovariance function of the data. That is all the possible information for Gaussian data, as well as the most important information for arbitrarily distributed data. A single model type and order is selected from many candidate time series models by looking for the smallest prediction error. The single selected model precisely includes only the statistically significant details that are present in the data. The residuals of the automatically selected time series model reveal the location of outliers or other irregularities that may not be visible in the measured signal. The program requires no user interaction and can be incorporated into automatic measurement instruments and protocols.