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Unified asymptotic theory for nearly unstable AR(p) processes

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  • Buchmann, Boris
  • Chan, Ngai Hang

Abstract

A unified asymptotic theory for nearly unstable higher order autoregressive processes and their least squares estimates is established. A novel version of Jordan’s canonical decomposition with perturbations together with a suitable plug-in principle is proposed to develop the underlying theories. Assumptions are stated in terms of the domain of attraction of partial Fourier transforms. The machinery is applied to recapture some of the classical results with the driving noise being martingale differences. Further, we show how to extend the results to higher order fractional ARIMA models in nearly unstable settings, thereby offering a comprehensive theory to analyse nearly unstable time series.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:123:y:2013:i:3:p:952-985
    DOI: 10.1016/j.spa.2012.09.014
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    References listed on IDEAS

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    1. Hidalgo, Javier, 2005. "Semiparametric estimation for stationary processes whose spectra have an unknown pole," LSE Research Online Documents on Economics 6842, London School of Economics and Political Science, LSE Library.
    2. Javier Hidalgo, 2005. "Semiparametric Estimation for Stationary Processes whose Spectra have an Unknown Pole," STICERD - Econometrics Paper Series 481, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Jeganathan, P., 1991. "On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 7(3), pages 269-306, September.
    4. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    5. Sofia C. Olhede, 2004. "Large-sample properties of the periodogram estimator of seasonally persistent processes," Biometrika, Biometrika Trust, vol. 91(3), pages 613-628, September.
    6. Davidson, James & Hashimzade, Nigar, 2009. "Representation And Weak Convergence Of Stochastic Integrals With Fractional Integrator Processes," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1589-1624, December.
    7. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(4), pages 583-621, August.
    8. 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.
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