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Moderate Deviation Principles for Empirical Covariance in the Neighbourhood of the Unit Root

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  • Yu Miao
  • Yanling Wang
  • Guangyu Yang

Abstract

type="main" xml:id="sjos12104-abs-0001"> In this paper, we consider the linear autoregressive model with varying coefficients θ n ∈[0,1). When θ n tending to the unit root, the moderate deviation principle for empirical covariance is discussed, and as statistical applications, we provide the moderate deviation estimates of the least square and the Yule–Walker estimators of the parameter θ n .

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:1:p:234-255
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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.
    2. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, January.
    3. 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.
    4. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    5. Chen, Xia, 1997. "Moderate deviations for m-dependent random variables with Banach space values," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 123-134, September.
    6. Mas, André & Menneteau, Ludovic, 2003. "Large and moderate deviations for infinite-dimensional autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 241-260, November.
    7. 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.
    8. Menneteau, Ludovic, 2005. "Some laws of the iterated logarithm in Hilbertian autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 405-425, February.
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    Cited by:

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    3. 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).
    4. Nannan Ma & Hailin Sang & Guangyu Yang, 2023. "Least absolute deviation estimation for AR(1) processes with roots close to unity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 799-832, October.

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