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M-estimation for Moderate Deviations From a Unit Root

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  • Xin-Bing Kong

Abstract

Phillips and Magdalinos (2007) introduced a larger neighborhoods of one (called moderate deviations) than the conventional local to unity roots in autoregression models. Least square estimates (LSE) of the serial correlation coefficient were studied and asymptotics were provided. In this article, we investigate the M-estimation of the serial correlation coefficient having moderate deviations from the unit root. For both the near stationary case and explosive case, the Bahadur representations and limits in distribution are given for the M-estimators of the serial correlation coefficient. The limit theory demonstrates that the convergence rates of the M-estimators are the same as that for LSE hence bridging the very different convergence rates of the stationary and unit root cases. The limit theory also facilitates the comparison of the relative asymptotic efficiency among different estimators within the family of M-estimators.

Suggested Citation

  • Xin-Bing Kong, 2015. "M-estimation for Moderate Deviations From a Unit Root," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(3), pages 476-485, February.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:3:p:476-485
    DOI: 10.1080/03610926.2012.751114
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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.

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