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Large and moderate deviations upper bounds for the Gaussian autoregressive process

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  • Worms, Julien

Abstract

We study the least-squares estimator in the scalar autoregressive model of order 1 with Gaussian noise and arbitrary fixed initial state. Upper bounds of both large and moderate deviations principles are achieved in the unstable and explosive frameworks. The moderate deviations results are consistent with known results of convergence in distribution of the literature.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:51:y:2001:i:3:p:235-243
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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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    Cited by:

    1. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
    2. 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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