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A Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes

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  • Davidson, James

Abstract

A central limit theorem is proved for dependent stochastic processes. Global heterogeneity of the distribution of the terms is permitted, including asymptotically unbounded moments. The approach is to adapt a CLT for martingale differences due to McLeish and show that suitably defined Bernstein blocks satisfy the required conditions.

Suggested Citation

  • Davidson, James, 1992. "A Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes," Econometric Theory, Cambridge University Press, vol. 8(3), pages 313-329, September.
    • Handle: RePEc:cup:etheor:v:8:y:1992:i:03:p:313-329_01
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    Cited by:

    1. William Dunsmuir & Jieyi He, 2017. "Marginal Estimation of Parameter Driven Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 120-144, January.
    2. Blasques, Francisco & van Brummelen, Janneke & Koopman, Siem Jan & Lucas, André, 2022. "Maximum likelihood estimation for score-driven models," Journal of Econometrics, Elsevier, vol. 227(2), pages 325-346.
    3. Donald W. K. Andrews & C. John McDermott, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(3), pages 343-360.
    4. Blais, Michel & MacGibbon, Brenda & Roy, Roch, 2000. "Limit theorems for regression models of time series of counts," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 161-168, January.
    5. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2019. "Analyzing variance in central limit theorems," MPRA Paper 101685, University Library of Munich, Germany.
    6. Yang, Lixiong & Lee, Chingnun & Shie, Fu Shuen, 2014. "How close a relationship does a capital market have with other markets? A reexamination based on the equal variance test," Pacific-Basin Finance Journal, Elsevier, vol. 26(C), pages 198-226.
    7. 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.
    8. Ghannam, Mai & Nkurunziza, Sévérien, 2023. "Tensor Stein-rules in a generalized tensor regression model," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    9. 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.
    10. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
    11. Gençay, Ramazan & Signori, Daniele, 2015. "Multi-scale tests for serial correlation," Journal of Econometrics, Elsevier, vol. 184(1), pages 62-80.
    12. Rongning Wu & Yunwei Cui, 2014. "A Parameter-Driven Logit Regression Model For Binary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 462-477, August.
    13. Calhoun, Gray, 2014. "Block Bootstrap Consistency Under Weak Assumptions," Staff General Research Papers Archive 34313, Iowa State University, Department of Economics.
    14. Cosme Vodounou, 1998. "Inférence fondée sur les statistiques des rendements de long terme," CIRANO Working Papers 98s-20, CIRANO.
    15. 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.
    16. Li, Yong & Yu, Jun & Zeng, Tao, 2020. "Deviance information criterion for latent variable models and misspecified models," Journal of Econometrics, Elsevier, vol. 216(2), pages 450-493.
    17. Jonathan B. Hill, 2005. "On Tail Index Estimation for Dependent, Heterogenous Data," Econometrics 0505005, University Library of Munich, Germany, revised 24 Mar 2006.
    18. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    19. Wu, Rongning & Cao, Jiguo, 2011. "Blockwise empirical likelihood for time series of counts," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 661-673, March.
    20. Shang, Zuofeng, 2012. "On latent process models in multi-dimensional space," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1259-1266.

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