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Sample Means, Sample Autocovariances, And Linear Regression Of Stationary Multivariate Long Memory Processes

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  • Chung, Ching-Fan

Abstract

We develop an asymptotic theory for the first two sample moments of a stationary multivariate long memory process under fairly general conditions. In this theory the convergence rates and the limits (the fractional Brownian motion, the Rosenblatt process, etc.) all depend intrinsically on the degree of long memory in the process. The theory of the sample moments is then applied to the multiple linear regression model. An interesting finding is that, even though all the regressors and the disturbance are stationary and ergodic, the joint long memory in one single regressor and in the disturbance can invalidate the usual asymptotic theory for the ordinary least squares (OLS) estimation. Specifically, the convergence rates of the OLS estimators become slower, the limits are not normal, and the standard t- and F-tests all collapse.

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  • Chung, Ching-Fan, 2002. "Sample Means, Sample Autocovariances, And Linear Regression Of Stationary Multivariate Long Memory Processes," Econometric Theory, Cambridge University Press, vol. 18(1), pages 51-78, February.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:51-78_18
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    Cited by:

    1. Richard T. Baillie & George Kapetanios & Fotis Papailias, 2017. "Inference for impulse response coefficients from multivariate fractionally integrated processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 60-84, March.
    2. Jen-Je Su, 2003. "On the power of the multivariate KPSS test of stationarity against fractionally integrated alternatives," Applied Economics Letters, Taylor & Francis Journals, vol. 10(10), pages 637-641.
    3. Jan Beran & Klaus Telkmann, 2021. "On inference for modes under long memory," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 429-455, June.
    4. Torben G. Andersen & Rasmus T. Varneskov, 2018. "Consistent Inference for Predictive Regressions in Persistent VAR Economies," CREATES Research Papers 2018-09, Department of Economics and Business Economics, Aarhus University.
    5. Ting Zhang & Hwai-Chung Ho & Martin Wendler & Wei Biao Wu, 2013. "Block Sampling under Strong Dependence," Papers 1312.5807, arXiv.org.
    6. Hsieh, Meng-Chen & Hurvich, Clifford M. & Soulier, Philippe, 2007. "Asymptotics for duration-driven long range dependent processes," Journal of Econometrics, Elsevier, vol. 141(2), pages 913-949, December.
    7. Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.
    8. Hongshuai Dai, 2013. "Convergence in Law to Operator Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 26(3), pages 676-696, September.
    9. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    10. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2010. "A two-sample test for comparison of long memory parameters," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2118-2136, October.
    11. Chung, Ching-Fan, 2001. "Calculating and analyzing impulse responses for the vector ARFIMA model," Economics Letters, Elsevier, vol. 71(1), pages 17-25, April.
    12. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2009. "Covariance function of vector self-similar processes," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2415-2421, December.
    13. Dalkir, Mehmet, 2010. "Spurious correlation under fractional integration in output series," Economics Letters, Elsevier, vol. 107(2), pages 165-168, May.
    14. Leschinski, Christian, 2017. "On the memory of products of long range dependent time series," Economics Letters, Elsevier, vol. 153(C), pages 72-76.
    15. Wenjie Wang & Yichong Zhang, 2024. "Gradient Wild Bootstrap for Instrumental Variable Quantile Regressions with Weak and Few Clusters," Papers 2408.10686, arXiv.org.
    16. Valdério Anselmo Reisen & Céline Lévy-Leduc & Edson Zambon Monte & Pascal Bondon, 2024. "A dimension reduction factor approach for multivariate time series with long-memory: a robust alternative method," Statistical Papers, Springer, vol. 65(5), pages 2865-2886, July.
    17. Düker, Marie-Christine, 2020. "Limit theorems in the context of multivariate long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5394-5425.
    18. Sibbertsen, Philipp & Wenger, Kai & Wingert, Simon, 2020. "Testing for Multiple Structural Breaks in Multivariate Long Memory Time Series," Hannover Economic Papers (HEP) dp-676, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    19. Bensalma, Ahmed, 2018. "Two Distinct Seasonally Fractionally Differenced Periodic Processes," MPRA Paper 84969, University Library of Munich, Germany.
    20. Farzad Sabzikar & Qiying Wang & Peter C.B. Phillips, 2018. "Asymptotic Theory for Near Integrated Process Driven by Tempered Linear Process," Cowles Foundation Discussion Papers 2131, Cowles Foundation for Research in Economics, Yale University.

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