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Regression Quantiles and Related Processes Under Long Range Dependent Errors

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  • Koul, H. L.
  • Mukherjee, K.

Abstract

This paper obtains asymptotic representations of the regression quantiles and the regression rank-scores processes in linear regression setting when the errors are a function of Gaussian random variables that ale stationary and long range dependent. These representations are then used to obtain the limiting behavior of L- and linear regression rank-scores statistics based on the above processes. The paper also obtains the asymptotic uniform linearity of the linear regression rank-scores processes and statistics based on residuals under the long range dependent setup. It thus generalizes some of the results of Jurecková [In Proceedings of the Meeting on Nonparametric Statistics and Related topics (A. K. Md. E. Saleh, Ed.) pp. 217-228. Elsevier, Amsterdam/New York] and Gutenbrunner and Jurecková [Ann. Statist. 20 305-329] for the case of independent errors to one of the highly useful dependent errors setup.

Suggested Citation

  • Koul, H. L. & Mukherjee, K., 1994. "Regression Quantiles and Related Processes Under Long Range Dependent Errors," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 318-337, November.
    • Handle: RePEc:eee:jmvana:v:51:y:1994:i:2:p:318-337
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    Cited by:

    1. Lijuan Huo & Tae-Hwan Kim & Yunmi Kim, 2013. "Testing for Autocorrelation in Quantile Regression Models," Working papers 2013rwp-54, Yonsei University, Yonsei Economics Research Institute.
    2. Yaeji Lim & Hee-Seok Oh, 2022. "Quantile spectral analysis of long-memory processes," Empirical Economics, Springer, vol. 62(3), pages 1245-1266, March.
    3. Hongtao Guo & Miranda S. Lam & Guojun Wu & Zhijie Xiao, 2013. "Risk Analysis Using Regression Quantiles: Evidence from International Equity Markets," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 7(2), pages 1-15.
    4. Chen, Shijie & Mukherjee, Kanchan, 1999. "Asymptotic uniform linearity of some robust statistics under exponentially subordinated strongly dependent models," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 137-146, August.
    5. Leonenko, Nikolai N. & Sharapov, Michail M. & El-Bassiouny, Ahmed H., 2000. "On the exactness of normal approximation of LSE of regression coefficient of long-memory random fields," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 121-130, June.
    6. Mohsin, Muhammad & Taghizadeh-Hesary, Farhad & Shahbaz, Muhammad, 2022. "Nexus between financial development and energy poverty in Latin America," Energy Policy, Elsevier, vol. 165(C).
    7. N. N. Leonenko & Emanuele Taufer, 2001. "Asymptotic properties of LSE in multivariate continuous regression with long memory stationary errors," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 54-71.
    8. Haiqi Li & Sung Yong Park & Joo Hwan Seo, 2011. "Quantile Elasticity of International Tourism Demand for South Korea Using the Quantile Autoregressive Distributed Lag Model," Tourism Economics, , vol. 17(5), pages 997-1015, October.
    9. Nikolai Leonenko & Emanuele Taufer, 2001. "On the rate of convergence to the Normal approximation of LSE in multiple regression with long memory random fields," Quaderni DISA 044, Department of Computer and Management Sciences, University of Trento, Italy, revised 12 Sep 2003.
    10. Mukherjee, Kanchan, 2000. "Linearization Of Randomly Weighted Empiricals Under Long Range Dependence With Applications To Nonlinear Regression Quantiles," Econometric Theory, Cambridge University Press, vol. 16(3), pages 301-323, June.
    11. repec:wyi:journl:002126 is not listed on IDEAS
    12. Zhao Chen & Runze Li & Yaohua Wu, 2012. "Weighted quantile regression for AR model with infinite variance errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 715-731.
    13. He, Fengyang & Wang, Huixia Judy & Zhou, Yuejin, 2022. "Extremal quantile autoregression for heavy-tailed time series," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).

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