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ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR(p) PROCESSES

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  • van der Meer, Tjacco
  • Pap, Gyula
  • van Zuijlen, Martien C.A.

Abstract

In this paper nearly unstable AR(p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behavior of the least-squares estimators of the coefficients. A convergence result is presented for the general complex-valued case. The limit distribution is given by the help of some continuous time AR processes. We apply the results for real-valued nearly unstable AR(p) models. In this case the limit distribution can be identified with the maximum likelihood estimator of the coefficients of the corresponding continuous time AR processes.

Suggested Citation

  • van der Meer, Tjacco & Pap, Gyula & van Zuijlen, Martien C.A., 1999. "ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR(p) PROCESSES," Econometric Theory, Cambridge University Press, vol. 15(2), pages 184-217, April.
    • Handle: RePEc:cup:etheor:v:15:y:1999:i:02:p:184-217_15
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    Cited by:

    1. Buchmann, Boris & Chan, Ngai Hang, 2013. "Unified asymptotic theory for nearly unstable AR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 952-985.
    2. Barczy, M. & Ispány, M. & Pap, G., 2011. "Asymptotic behavior of unstable INAR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 583-608, March.
    3. E. E. Ioannidis & G. A. Chronis, 2005. "Extreme Spectra of Var Models and Orders of Near‐Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 399-421, May.
    4. Ling, Shiqing & McAleer, Michael, 2004. "Regression quantiles for unstable autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 304-328, May.
    5. Jui-Chung Yang & Ke-Li Xu, 2013. "Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function," 2013 Papers pya307, Job Market Papers.

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