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Fixed accuracy estimation of parameters in a threshold autoregressive model

Author

Listed:
  • Victor V. Konev

    (Tomsk State University)

  • Sergey E. Vorobeychikov

    (Tomsk State University)

Abstract

For parameters in a threshold autoregressive process, the paper proposes a sequential modification of the least squares estimates with a specific stopping rule for collecting the data for each parameter. In the case of normal residuals, these estimates are exactly normally distributed in a wide range of unknown parameters. On the base of these estimates, a fixed-size confidence ellipsoid covering true values of parameters with prescribed probability is constructed. In the i.i.d. case with unspecified error distributions, the sequential estimates are asymptotically normally distributed uniformly in parameters belonging to any compact set in the ergodicity parametric region. Small-sample behavior of the estimates is studied via simulation data.

Suggested Citation

  • Victor V. Konev & Sergey E. Vorobeychikov, 2022. "Fixed accuracy estimation of parameters in a threshold autoregressive model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 685-711, August.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:4:d:10.1007_s10463-021-00812-4
    DOI: 10.1007/s10463-021-00812-4
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    References listed on IDEAS

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    1. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
    2. Lai, T. L. & Wei, C. Z., 1983. "Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 1-23, March.
    3. Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2013. "Estimation in threshold autoregressive models with a stationary and a unit root regime," Journal of Econometrics, Elsevier, vol. 172(1), pages 1-13.
    4. Chun Yip Yau & Chong Man Tang & Thomas C. M. Lee, 2015. "Estimation of Multiple-Regime Threshold Autoregressive Models With Structural Breaks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1175-1186, September.
    5. P. Chigansky & Yu. Kutoyants, 2013. "Estimation in threshold autoregressive models with correlated innovations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 959-992, October.
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