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Strong Laws for Dependent Heterogeneous Processes

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  • Hansen, Bruce E.

Abstract

This paper presents maximal inequalities and strong law of large numbers for weakly dependent heterogeneous random variables. Specifically considered are Lr mixingales for r > 1, strong mixing sequences, and near epoch dependent (NED) sequences. We provide the first strong law for Lr-bounded Lr mixingales and NED sequences for 1 > r > 2. The strong laws presented for α-mixing sequences are less restrictive than the laws of McLeish [8].

Suggested Citation

  • Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(2), pages 213-221, June.
    • Handle: RePEc:cup:etheor:v:7:y:1991:i:02:p:213-221_00
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    Citations

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    Cited by:

    1. Caner,M. & Hansen,B.E., 1998. "Threshold autoregression with a near unit root," Working papers 27, Wisconsin Madison - Social Systems.
    2. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    3. Yaein Baek, 2018. "Estimation of a Structural Break Point in Linear Regression Models," Papers 1811.03720, arXiv.org, revised Jun 2020.
    4. Smeekes, S. & Urbain, J.R.Y.J., 2014. "A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing," Research Memorandum 008, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Fiteni, Inmaculada, 2004. "[tau]-estimators of regression models with structural change of unknown location," Journal of Econometrics, Elsevier, vol. 119(1), pages 19-44, March.
    6. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, vol. 70(1), pages 99-126, January.
    7. Meng, Yanjiao & Lin, Zhengyan, 2009. "Maximal inequalities and laws of large numbers for Lq-mixingale arrays," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1539-1547, July.
    8. Friedrich, Marina & Smeekes, Stephan & Urbain, Jean-Pierre, 2020. "Autoregressive wild bootstrap inference for nonparametric trends," Journal of Econometrics, Elsevier, vol. 214(1), pages 81-109.
    9. Yang, Wenzhi & Hu, Shuhe, 2014. "Large deviation for a least squares estimator in a nonlinear regression model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 135-144.
    10. Banerjee Anurag & Pitarakis Jean-Yves, 2014. "Functional cointegration: definition and nonparametric estimation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 1-14, December.
    11. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.
    12. Adamek, Robert & Smeekes, Stephan & Wilms, Ines, 2023. "Lasso inference for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 235(2), pages 1114-1143.
    13. de Jong, Robert M., 1996. "A strong law of large numbers for triangular mixingale arrays," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 1-9, March.
    14. Gonçalves, Sílvia & White, Halbert, 2002. "The Bootstrap Of The Mean For Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1367-1384, December.
    15. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    16. PREMINGER, Arie & HAFNER, Christian, 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," LIDAM Discussion Papers CORE 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Jong, R.M., 1991. "Laws of large numbers for dependent heterogeneous processes," Serie Research Memoranda 0088, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    18. Chaohua Dong & Jiti Gao & Bin Peng & Yayi Yan, 2023. "Estimation and Inference for a Class of Generalized Hierarchical Models," Papers 2311.02789, arXiv.org, revised Apr 2024.
    19. repec:bgu:wpaper:0603 is not listed on IDEAS
    20. Peter Farkas & Laszlo Matyas, 2015. "Testing for Unit Roots in Panel Data with Boundary Crossing Counts," CEU Working Papers 2015_5, Department of Economics, Central European University, revised 03 Nov 2015.
    21. Anirvan Chakraborty & Probal Chaudhuri, 2014. "On data depth in infinite dimensional spaces," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 303-324, April.
    22. Chaohua Dong & Jiti Gao & Bin Peng & Yayi Yan, 2023. "Estimation of Semiparametric Multi-Index Models Using Deep Neural Networks," Monash Econometrics and Business Statistics Working Papers 21/23, Monash University, Department of Econometrics and Business Statistics.

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