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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 L r mixingales for r > 1, strong mixing sequences, and near epoch dependent (NED) sequences. We provide the first strong law for L r -bounded L r 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(02), pages 213-221, June.
  • Handle: RePEc:cup:etheor:v:7:y:1991:i:02:p:213-221_00
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    References listed on IDEAS

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    1. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, pages 1047-1070.
    2. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, pages 229-256.
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    Cited by:

    1. Mehmet Caner & Bruce E. Hansen, 1998. "Threshold Autoregressions with a Near Unit Root," Working Papers 9821, Department of Economics, Bilkent University.
    2. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, pages 575-604.
    3. Driesen, Bram & Lombardi, Michele & Peters, Hans, 2016. "Feasible sets, comparative risk aversion, and comparative uncertainty aversion in bargaining," Journal of Mathematical Economics, Elsevier, pages 162-170.
    4. Fiteni, Inmaculada, 2004. "[tau]-estimators of regression models with structural change of unknown location," Journal of Econometrics, Elsevier, pages 19-44.
    5. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, pages 99-126.
    6. Meng, Yanjiao & Lin, Zhengyan, 2009. "Maximal inequalities and laws of large numbers for Lq-mixingale arrays," Statistics & Probability Letters, Elsevier, pages 1539-1547.
    7. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, pages 167-176.
    8. Yang, Wenzhi & Hu, Shuhe, 2014. "Large deviation for a least squares estimator in a nonlinear regression model," Statistics & Probability Letters, Elsevier, pages 135-144.
    9. Yeon-Koo Che & József Sákovics, 2004. "A Dynamic Theory of Holdup," Econometrica, Econometric Society, pages 1063-1103.
    10. Banerjee Anurag & Pitarakis Jean-Yves, 2014. "Functional cointegration: definition and nonparametric estimation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, pages 1-14.
    11. Shin Kanaya, 2016. "Convergence rates of sums of a-mixing triangular arrays: with an application to non-parametric drift function estimation of continuous-time processes," CREATES Research Papers 2016-24, Department of Economics and Business Economics, Aarhus University.
    12. de Jong, Robert M., 1996. "A strong law of large numbers for triangular mixingale arrays," Statistics & Probability Letters, Elsevier, pages 1-9.
    13. Gon alves, S lvia & White, Halbert, 2002. "The Bootstrap Of The Mean For Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, pages 1367-1384.
    14. 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.
    15. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, pages 821-856.
    16. 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.
    17. Gon alves, S lvia & White, Halbert, 2002. "The Bootstrap Of The Mean For Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, pages 1367-1384.
    18. Goncalves, S. & White, H., 2001. "The Bootstrap of Mean for Dependent Heterogeneous Arrays," Cahiers de recherche 2001-19, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    19. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, pages 575-604.
    20. PREMINGER, Arie & HAFNER, Christian M., 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," CORE Discussion Papers 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    21. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, pages 821-856.
    22. Arie Preminger & Christian M. Hafner, 2006. "Deciding Between Garch And Stochastic Volatility Via Strong Decision Rules," Working Papers 0603, Ben-Gurion University of the Negev, Department of Economics.
    23. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, pages 99-126.
    24. 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.
    25. 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, pages 303-324.

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