Identification of nonstationarity for autoregressive models

The paper is concerned with the identification problem of nonstationarity for autoregressive models. Several principles are proposed and used as criteria to identify the nonstationarity for autoregressive models, with the largest multiplicity of all the distinct roots on the unit cycle being determined by the criteria when the corresponding model is nonstationary. The necessary and sufficient conditions for an autoregressive model to be asymptotically stationary are given