A Class of Modified High-Order Autoregressive Models with Improved Resolution of Low-Frequency Cycles

We consider regularly sampled processes that have most of their spectral power at low frequencies. A simple example of such a process is used to demonstrate that the standard autoregressive (AR) model, with its order selected by an information criterion, can provide a poor approximation to the process. In particular, it can result in poor multi-step predictions. We propose instead the use of a class of pth order AR models obtained by the addition of a pre-specified pth order moving average term. We present a re-parameterization of this model and show that with a low order it can provide a very good approximation to the process and its multi-step predictions. Methods of model identification and estimation are presented, based on a transformed sample spectrum, and modified partial autocorrelations. The method is also illustrated on a real example