Asymptotically efficient order selection in nonstationary AR processes
Date
2000ISSN
1133-0686Source
TestVolume
9Issue
2Pages
371-391Google Scholar check
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In this paper we investigate the issue of asymptotic efficiency in nonstationary AR(∞) processes. Since the inverse of the autocovariance matrix of the underlying process cannot be evaluated due to the fact that the matrix is singular, traditional methods and techniques (Karagrigoriou 1995, 1997 Bhansali 1996) cannot be applied. Here we attempt to reduce the nonstationary case to a stationary one so that known results can then be applied to the reduced process. Asymptotic results regarding the overestimation of the order of an AR process with several unit roots are presented and the asymptotic efficiency of the order selected is established in the case where d (d > 0) unit roots are present.