Selection of type and order of time series models

New developments in time series analysis can be used to determine a better representation for stochastic processes. Three model types are: autoregressive (AR), moving average (MA) and the combined ARMA models. In theory, time series models present an excellent solution if the model type and model order are known. In practice, however, the best model type and order are unknown. A proper selection is possible only if the three model types have been estimated with suitable algorithms; this means that the stationary and invertible models must be computed for all orders, even when only a small number of observations is available. With only the measured data as input, a single time series model is selected without prejudice. The selected model characterizes the data with its covariance function or spectral density; the same model can also be used for feature extraction