Estimating and Applying Autoregression Models via Their Eigensystem Representation

This article introduces the eigensystem autoregression (EAR) framework, which allows an AR model to
be specified, estimated, and applied directly in terms of its eigenvalues and eigenvectors. An EAR
estimation can therefore impose various constraints on AR dynamics that would not be possible within
standard linear estimation. Examples are restricting eigenvalue magnitudes to control the rate of mean
reversion, additionally imposing that eigenvalues be real and positive to avoid pronounced oscillatory
behavior, and eliminating the possibility of explosive episodes in a time-varying AR. The EAR framework
also produces closed-form AR forecasts and associated variances, and forecasts and data may be
decomposed into components associated with the AR eigenvalues to provide additional diagnostics for
assessing the model.