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Large deviations for the Yule–Walker estimator of near critical autoregressive processes

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  • Wang, Xiaochang
  • Feng, Shui
  • Guo, Yiping
  • Rémillard, Bruno N.

Abstract

The large deviation principle is established for the Yule–Walker estimator of the near critical order one autoregressive process. The rate function is identified explicitly. Our result shows that, at the exponential scale, one cannot distinguish between near critical and the critical Yule–Walker estimators.

Suggested Citation

  • Wang, Xiaochang & Feng, Shui & Guo, Yiping & Rémillard, Bruno N., 2024. "Large deviations for the Yule–Walker estimator of near critical autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 214(C).
    • Handle: RePEc:eee:stapro:v:214:y:2024:i:c:s0167715224001652
    DOI: 10.1016/j.spl.2024.110196
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    References listed on IDEAS

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    1. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Bercu, B. & Gamboa, F. & Rouault, A., 1997. "Large deviations for quadratic forms of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 75-90, October.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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