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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. 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.
    3. Cosme Vodounou, 1998. "Inférence fondée sur les statistiques des rendements de long terme," CIRANO Working Papers 98s-20, CIRANO.
    4. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    5. 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.
    6. 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.
    7. Shang, Zuofeng, 2012. "On latent process models in multi-dimensional space," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1259-1266.
    8. 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.
    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. Alessio Sancetta, 2023. "Intraday Trades Profile Estimation: An Intensity Approach," Journal of Financial Econometrics, Oxford University Press, vol. 21(3), pages 651-677.
    11. 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.
    12. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2019. "Analyzing variance in central limit theorems," MPRA Paper 101685, University Library of Munich, Germany.
    13. Ghannam, Mai & Nkurunziza, Sévérien, 2023. "Tensor Stein-rules in a generalized tensor regression model," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    14. Gençay, Ramazan & Signori, Daniele, 2015. "Multi-scale tests for serial correlation," Journal of Econometrics, Elsevier, vol. 184(1), pages 62-80.
    15. Calhoun, Gray, 2014. "Block Bootstrap Consistency Under Weak Assumptions," Staff General Research Papers Archive 34313, Iowa State University, Department of Economics.
    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. 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.
    18. 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.
    19. 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.
    20. 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.
    21. Jonathan B. Hill, 2005. "On Tail Index Estimation for Dependent, Heterogenous Data," Econometrics 0505005, University Library of Munich, Germany, revised 24 Mar 2006.

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