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Limit distributions for linear programming time series estimators

Author

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  • Feigin, Paul D.
  • Resnick, Sidney I.

Abstract

We consider stationary autoregressive processes of order p which have positive innovations. We propose consistent parameter estimators based on linear programming. Under conditions, including regular variation of either the left or right tail of the innovations distribution, we prove that the estimators have a limit distribution. The rate of convergence of our estimator is favorable compared with the Yule--Walker estimator under comparable circumstances.

Suggested Citation

  • Feigin, Paul D. & Resnick, Sidney I., 1994. "Limit distributions for linear programming time series estimators," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 135-165, June.
    • Handle: RePEc:eee:spapps:v:51:y:1994:i:1:p:135-165
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    Citations

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    Cited by:

    1. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
    2. Brown, Tim C. & Feigin, Paul D. & Pallant, Diana L., 1996. "Estimation for a class of positive nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 139-152, November.
    3. Jana Jurečková & Hira Koul & Jan Picek, 2009. "Testing the tail index in autoregressive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 579-598, September.
    4. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.
    5. Preve, Daniel & Medeiros, Marcelo C., 2011. "Linear programming-based estimators in simple linear regression," Journal of Econometrics, Elsevier, vol. 165(1), pages 128-136.
    6. Victor Chernozhukov & Iván Fernández-Val, 2011. "Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 559-589.
    7. repec:aaa:journl:v:3:y:1999:i:1:p:87-100 is not listed on IDEAS
    8. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    9. Allen, Michael R. & Datta, Somnath, 1999. "Estimation of the index parameter for autoregressive data using the estimated innovations," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 315-324, February.
    10. Joseph Altonji & Hidehiko Ichimura & Taisuke Otsu, 2019. "Nonparametric intermediate order regression quantiles," STICERD - Econometrics Paper Series 608, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. Knight, Keith, 2003. "Asymptotic theory for M-estimators of boundaries," SFB 373 Discussion Papers 2003,37, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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