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Cramér’s moderate deviations for the LS estimator of the autoregressive processes in the neighborhood of the unit root

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  • Miao, Yu
  • Yin, Qing

Abstract

In this paper, we consider the linear autoregressive model with varying coefficients θn tending to the unit root. Cramér’s moderate deviations of the least-squares estimator of the parameter θn is discussed.

Suggested Citation

  • Miao, Yu & Yin, Qing, 2024. "Cramér’s moderate deviations for the LS estimator of the autoregressive processes in the neighborhood of the unit root," Statistics & Probability Letters, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:stapro:v:209:y:2024:i:c:s0167715224000622
    DOI: 10.1016/j.spl.2024.110093
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    References listed on IDEAS

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    1. 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.
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    3. Worms, Julien, 2001. "Large and moderate deviations upper bounds for the Gaussian autoregressive process," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 235-243, February.
    4. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    5. Yu Miao & Yanling Wang & Guangyu Yang, 2015. "Moderate Deviation Principles for Empirical Covariance in the Neighbourhood of the Unit Root," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 234-255, March.
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