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Convergence Of Integral Functionals Of Stochastic Processes

Author

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  • Berkes, István
  • Horváth, Lajos

Abstract

We investigate the convergence in distribution of integrals of stochastic processes satisfying a functional limit theorem. We allow a large class of continuous Gaussian processes in the limit. Depending on the continuity properties of the underlying process, local Lebesgue or Riemann integrability is required.We are grateful to the referees and Benedikt Pötscher for their helpful and constructive comments. The research of the first author was partially supported by OTKA grants T37668 and T43037 and NSF-OTKA grant INT-0223262. The research of the second author was partially supported by NATO grant PST.EAP.CLG 980599 and NSF-OTKA grant INT-0223262.

Suggested Citation

  • Berkes, István & Horváth, Lajos, 2006. "Convergence Of Integral Functionals Of Stochastic Processes," Econometric Theory, Cambridge University Press, vol. 22(2), pages 304-322, April.
  • Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:304-322_06
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    Cited by:

    1. Jiti Gao & Peter C.B. Phillips, 2011. "Semiparametric Estimation in Multivariate Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 17/11, Monash University, Department of Econometrics and Business Statistics.
    2. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    3. Zongwu Cai & Bingyi Jing & Xinbing Kong & Zhi Liu, 2017. "Nonparametric regression with nearly integrated regressors under long‐run dependence," Econometrics Journal, Royal Economic Society, vol. 20(1), pages 118-138, February.
    4. Pötscher, Benedikt M., 2013. "On The Order Of Magnitude Of Sums Of Negative Powers Of Integrated Processes," Econometric Theory, Cambridge University Press, vol. 29(3), pages 642-658, June.
    5. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1466-1497, December.
    6. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
    7. Berenguer Rico, Vanessa & Gonzalo, Jesús, 2013. "Co-summability from linear to non-linear cointegration," UC3M Working papers. Economics we1312, Universidad Carlos III de Madrid. Departamento de Economía.
    8. Chan, Nigel & Wang, Qiying, 2015. "Nonlinear regressions with nonstationary time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 182-195.
    9. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1466-1497, December.
    10. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
    11. Zhishui Hu & Peter C.B. Phillips & Qiying Wang, 2019. "Nonlinear Cointegrating Power Function Regression with Endogeneity," Cowles Foundation Discussion Papers 2211, Cowles Foundation for Research in Economics, Yale University.
    12. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    13. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
    14. repec:wyi:journl:002096 is not listed on IDEAS
    15. Berenguer-Rico, Vanessa & Gonzalo, Jesús, 2014. "Summability of stochastic processes—A generalization of integration for non-linear processes," Journal of Econometrics, Elsevier, vol. 178(P2), pages 331-341.
    16. Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, vol. 176(1), pages 59-79.

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