Let the Data Speak for Themselves

An estimation algorithm for stationary random data automatically selects a single time-series (TS) model for a given number of observations. The parameters of that model accurately represent the spectral density and the autocovariance function of the data. The increased computational speed has given the possibility to compute hundreds of TS models and to select only one. The computer program uses a selection criterion to determine the best model type and model order from a large number of candidates. That selected model includes all statistically significant details that are present in the data, and no more. The spectral density of high-order TS models is the same as the raw periodogram, and the autocorrelation function can be the same as the lagged product (LP) estimate. Therefore, the periodogram and the LP autocorrelation function are very high-order TS candidates. However, those high-order models are never selected in practice because they contain many insignificant details. The automatic selection with the algorithm lets the data speak for themselves: a single model is selected without user interaction. The automatic program can be implemented in measurement instruments for maintenance or in radar, by automatically detecting differences in signal properties