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Central Limit Theorems for Dependent Heterogeneous Random Variables

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  • de Jong, Robert M.

Abstract

This paper presents central limit theorems for triangular arrays of mixingale and near-epoch-dependent random variables. The central limit theorem for near-epoch-dependent random variables improves results from the literature in various respects. The approach is to define a suitable Bernstein blocking scheme and apply a martingale difference central limit theorem, which in combination with weak dependence conditions renders the result. The most important application of this central limit theorem is the improvement of the conditions that have to be imposed for asymptotic normality of minimization estimators.

Suggested Citation

  • de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(03), pages 353-367, June.
  • Handle: RePEc:cup:etheor:v:13:y:1997:i:03:p:353-367_00
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    Cited by:

    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    2. de Jong, Robert M. & Woutersen, Tiemen, 2011. "Dynamic Time Series Binary Choice," Econometric Theory, Cambridge University Press, vol. 27(04), pages 673-702, August.
    3. Manuel Landajo & María José Presno, 2010. "Stationarity testing under nonlinear models. Some asymptotic results," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 392-405, September.
    4. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    5. Kapetanios, G. & Pesaran, M. Hashem & Yamagata, T., 2011. "Panels with non-stationary multifactor error structures," Journal of Econometrics, Elsevier, vol. 160(2), pages 326-348, February.
    6. repec:hal:journl:peer-00768190 is not listed on IDEAS
    7. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    8. Calhoun, Gray, 2014. "Out-Of-Sample Comparisons of Overfit Models," Staff General Research Papers Archive 32462, Iowa State University, Department of Economics.
    9. repec:cup:etheor:v:33:y:2017:i:05:p:1046-1080_00 is not listed on IDEAS
    10. Qiu, Jin & Lin, Zhengyan, 2006. "The variance of partial sums of strong near-epoch dependent variables," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1845-1854, November.
    11. Clark, Todd E. & McCracken, Michael W., 2012. "In-sample tests of predictive ability: A new approach," Journal of Econometrics, Elsevier, vol. 170(1), pages 1-14.
    12. J. Isaac Miller, 2010. "Cointegrating regressions with messy regressors and an application to mixed-frequency series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 255-277, July.
    13. Donald W.K. Andrews, 2017. "Identification-Robust Subvector Inference," Cowles Foundation Discussion Papers 2105, Cowles Foundation for Research in Economics, Yale University, revised Sep 2017.
    14. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
    15. Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 553-574, November.
    16. repec:hal:journl:peer-00834423 is not listed on IDEAS
    17. Andreou, Elena & Ghysels, Eric, 2006. "Monitoring disruptions in financial markets," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 77-124.
    18. Calhoun, Gray, 2014. "Block Bootstrap Consistency Under Weak Assumptions," Staff General Research Papers Archive 34313, Iowa State University, Department of Economics.
    19. Shin S. Ikeda, 2013. "A Note on the Mixingale Limit Theorem by McLeish (1977)," GRIPS Discussion Papers 13-11, National Graduate Institute for Policy Studies.
    20. Andrews, Donald W.K. & Guggenberger, Patrik, 2017. "Asymptotic Size Of Kleibergen’S Lm And Conditional Lr Tests For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 33(05), pages 1046-1080, October.
    21. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    22. Hill, Jonathan B., 2010. "On Tail Index Estimation For Dependent, Heterogeneous Data," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1398-1436, October.
    23. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Journal of Econometrics, Elsevier, vol. 163(2), pages 215-230, August.
    24. Donald W.K. Andrews, 2017. "Identification-Robust Subvector Inference," Cowles Foundation Discussion Papers 3005, Cowles Foundation for Research in Economics, Yale University, revised Sep 2017.

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