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Limit Theory for Moderate Deviations from a Unit Root Under Innovations with a Possibly Infinite Variance

Author

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  • Sai-Hua Huang

    (Zhejiang University)

  • Tian-Xiao Pang

    (Zhejiang University)

  • Chengguo Weng

    (University of Waterloo)

Abstract

An asymptotic theory was given by Phillips and Magdalinos (J Econom 136(1):115–130, 2007) for autoregressive time series Y t = ρY t−1 + u t , t = 1,...,n, with ρ = ρ n = 1 + c/k n , under (2 + δ)-order moment condition for the innovations u t , where δ > 0 when c 0, {u t } is a sequence of independent and identically distributed random variables, and (k n ) n ∈ ℕ is a deterministic sequence increasing to infinity at a rate slower than n. In the present paper, we established similar results when the truncated second moment of the innovations $l(x)=\textsf{E} [u_1^2I\{|u_1|\le x\}]$ is a slowly varying function at ∞, which may tend to infinity as x → ∞. More interestingly, we proposed a new pivotal for the coefficient ρ in case c

Suggested Citation

  • Sai-Hua Huang & Tian-Xiao Pang & Chengguo Weng, 2014. "Limit Theory for Moderate Deviations from a Unit Root Under Innovations with a Possibly Infinite Variance," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 187-206, March.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:1:d:10.1007_s11009-012-9306-7
    DOI: 10.1007/s11009-012-9306-7
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Wang, Gaowen, 2006. "A note on unit root tests with heavy-tailed GARCH errors," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1075-1079, May.
    4. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
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    Cited by:

    1. Christis Katsouris, 2022. "Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions," Papers 2204.02073, arXiv.org, revised Aug 2023.
    2. Pang, Tianxiao & Tai-Leung Chong, Terence & Zhang, Danna & Liang, Yanling, 2018. "Structural Change In Nonstationary Ar(1) Models," Econometric Theory, Cambridge University Press, vol. 34(5), pages 985-1017, October.
    3. Bingqi Liu & Tianxiao Pang, 2024. "Weighted composite quantile inference for nearly nonstationary autoregressive models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(5), pages 1337-1379, November.

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