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Asymptotic Moments of Autoregressive Estimators with a Near Unit Root and Minimax Risk

In: Essays in Honor of Peter C. B. Phillips

Author

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  • Bruce E. Hansen

Abstract

These moments of the asymptotic distribution of the least-squares estimator of the local-to-unity autoregressive model are computed using computationally simple integration. These calculations show that conventional simulation estimation of moments can be substantially inaccurate unless the simulation sample size is very large. We also explore the minimax efficiency of autoregressive coefficient estimation, and numerically show that a simple Stein shrinkage estimator has minimax risk which is uniformly better than least squares, even though the estimation dimension is just one.

Suggested Citation

  • Bruce E. Hansen, 2014. "Asymptotic Moments of Autoregressive Estimators with a Near Unit Root and Minimax Risk," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 14, pages 3-21, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320140000033001
    DOI: 10.1108/S0731-905320140000033001
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    Cited by:

    1. Zhongwen Liang, 2017. "A Unified Approach on the Local Power of Panel Unit Root Tests," Papers 1710.02944, arXiv.org.

    More about this item

    Keywords

    Minimax; efficiency; unit root; autoregression; shrinkage; moments; C22;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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