ARMAsel as a Language for Random Data

Two different high order time series models represent a parametric spectral estimate that is exactly equal to the non-parametric periodogram. Hence, the raw material for parametric and for non-parametric spectral and autocorrelation analysis is the same. In non-parametric estimation, the periodogram is smoothed with a window to diminish or remove insignificant details. That gives a distortion to the details of all modified non-parametric estimates, defined by the shape and by the width of the window. In contrast, parametric time series models can eliminate higher order details without distorting the remaining lower order details. First, many candidate models are estimated, with different type and order. From those candidates, a single time series model is selected automatically, without user interaction. The selection of model order and model type with the ARMAsel algorithm lets the data speak and decide. Interesting alternative models are suggested by the estimated accuracies of all other candidates, in what can be called the language of the data