Acta Mathematicae Applicatae Sinica

, Volume 11, Issue 3, pp 225–239 | Cite as

Estimation of the parameters for unstable AR models

  • An Hongzhi 
  • Lie Guibin 


This paper is concerned with the unstable autoregressive process which satisfies the unstable autoregressive (AR) modelU(B)G(B)x t =ε t , where all the roots of the polynomialsU(z) andG(z) lie on and outside the unit circle respectively. We propose several procedures to estimate the coefficients ofU(z) andG(z) separately, in order to guarantee that the estimated polynomials ofU(z) andG(z) have all the roots lying on and outside the unit circle respectively. The estimators of the coefficients ofU(z) andG(z) are shown to be of strong consistency. The limiting distribution of the estimators of the coefficients ofU(B)G(B) are obtained for some special cases.

Key words

Unstable AR model estimation parameters strong consistency asymptotic distribution 


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Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1995

Authors and Affiliations

  • An Hongzhi 
    • 1
  • Lie Guibin 
    • 2
  1. 1.Institute of Applied Mathematicsthe Chinese Academy of ScienceBeijingChina
  2. 2.Department of Probability and StatisticsBeijing UniversityBeijingChina

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