, Volume 74, Issue 1, pp 55–66 | Cite as

Asymptotic inference for a one-dimensional simultaneous autoregressive model

  • Sándor BaranEmail author
  • Gyula Pap


A nonstationary simultaneous autoregressive model \({X^{(n)}_k=\alpha \Big(X^{(n)}_{k-1}+X^{(n)}_{k+1}\Big)+\varepsilon_k, k=1, 2, \ldots , n-1}\), is investigated, where \({X^{(n)}_0}\) and \({X^{(n)}_n}\) are given random variables. It is shown that in the unstable case α = 1/2 the least squares estimator of the autoregressive parameter converges to a functional of a standard Wiener process with a rate of convergence n 2, while in the stable situation |α| < 1/2 the estimator is biased but asymptotically normal with a rate n 1/2.


Simultaneous autoregressive models Asymptotically stationary model Martingale central limit theorem Unit roots Least squares estimator 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Faculty of InformaticsUniversity of DebrecenDebrecenHungary
  2. 2.Bolyai InstituteUniversity of SzegedSzegedHungary

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