Automatic spectral analysis with time series models

The increased computational speed and developments in the robustness of algorithms have created the possibility to identify automatically a well-fitting time series model for stochastic data. It is possible to compute more than 500 models and to select only one, which certainly is one of the better models, if not the very best. That model characterizes the spectral density of the data. Time series models are excellent for random data if the model type and the model order are known. For unknown data characteristics, a large number of candidate models have to be computed. This necessarily includes too low or too high model orders and models of the wrong types, thus requiring robust estimation methods. The computer selects a model order for each of the three model types. From those three, the model type with the smallest expectation of the prediction error is selected. That unique selected model includes precisely the statistically significant details that are present in the data.