Selection of type and order of time series models

摘要

New developments in time series analysis can be used to determinea 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 modeltype and model order are known. In practice, however, the best modeltype and order are unknown. A proper selection is possible only if thethree model types have been estimated with suitable algorithms; thismeans that the stationary and invertible models must be computed for allorders, even when only a small number of observations is available. Withonly the measured data as input, a single time series model is selectedwithout prejudice. The selected model characterizes the data with itscovariance function or spectral density; the same model can also be usedfor feature extraction