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Convergence Of Integral Functionals Of Stochastic Processes

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  • Berkes, Istv n
  • Horv th, Lajos
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    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 P tscher 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.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 22 (2006)
    Issue (Month): 02 (April)
    Pages: 304-322

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    Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:304-322_06

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    Cited by:
    1. Ioannis Kasparis & Peter C.B. Phillips, 2009. "Dynamic Misspecification in Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1700, Cowles Foundation for Research in Economics, Yale University.
    2. 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.
    3. Pötscher, Benedikt M., 2013. "On The Order Of Magnitude Of Sums Of Negative Powers Of Integrated Processes," Econometric Theory, Cambridge University Press, vol. 29(03), pages 642-658, June.
    4. repec:wyi:journl:002096 is not listed on IDEAS
    5. Vanessa Berenguer Rico & Jesús Gonzalo, 2013. "Co-summability from linear to non-linear cointegration," Economics Working Papers we1312, Universidad Carlos III, Departamento de Economía.
    6. Qiying Wang & Peter C.B. Phillips, 2006. "Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1594, Cowles Foundation for Research in Economics, Yale University.
    7. 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.
    8. Peter C.B. Phillips, 2008. "Local Limit Theory and Spurious Nonparametric Regression," Cowles Foundation Discussion Papers 1654, Cowles Foundation for Research in Economics, Yale University.
    9. repec:wyi:wpaper:002020 is not listed on IDEAS
    10. 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.
    11. 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.

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