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Mixing convergence of LSE for supercritical AR(2) processes with Gaussian innovations using random scaling

Author

Listed:
  • Mátyás Barczy

    (Bolyai Institute, University of Szeged)

  • Fanni Nedényi

    (Bolyai Institute, University of Szeged)

  • Gyula Pap

    (Bolyai Institute, University of Szeged)

Abstract

We prove mixing convergence of the least squares estimator of autoregressive parameters for supercritical autoregressive processes of order 2 with Gaussian innovations having real characteristic roots with different absolute values. We use an appropriate random scaling such that the limit distribution is a two-dimensional normal distribution concentrated on a one-dimensional ray determined by the characteristic root having the larger absolute value.

Suggested Citation

  • Mátyás Barczy & Fanni Nedényi & Gyula Pap, 2024. "Mixing convergence of LSE for supercritical AR(2) processes with Gaussian innovations using random scaling," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(6), pages 729-756, August.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:6:d:10.1007_s00184-023-00936-y
    DOI: 10.1007/s00184-023-00936-y
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    References listed on IDEAS

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    1. Datta, Somnath, 1995. "Limit theory and bootstrap for explosive and partially explosive autoregression," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 285-304, June.
    2. Monsour, Michael J., 2016. "Decomposition of an autoregressive process into first order processes," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 295-314.
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