ARMA models are a class of extremely important rational models. Selecting the model order is a critical first step toward the goal of modeling an ARMA process.
In this thesis, it is shown that the conventional methods fail to correctly determine the AR model order when the ratio of magnitude of two poles become large. When one or several poles are near the unit circle, it is hard to detect the presence of poles which have relatively smaller magnitude than them. To overcome this problem two methods are proposed.
The first is to reduce the effect of the poles near the unit circle by adding zeros to cancel out them. The magnitude of the poles can be estimated using settling time of data covariance, and the phase of the poles can be estimated using the bandwith of the peaks of power spectrum.
The second is to use the covariance of inverse ARMA(q,p) model to find the order of ARMA(p,q) model when no zeros are located close to the unit circle. Since the conventional methods can correctly determine the MA model order regardless the relations of zero, it possible to find the correct order using the covariance of inverse model. The covariance of inverse model can be obtained easily from the given data because the power spectrum of inverse model is the inverse of the power spectrum of original model.
Numerical examples are given and illustrate improved accuracy of the proposed methods.
