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Nonparametric Time Series Estimation of Joint DGP, Conditional DGP and Vector Autoregression

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  • Radhey S. Singh
  • Aman Ullah

Abstract

In this paper we develop nonparametric estimators of the joint time series data generating process (DGP) of (xt, yt) at different t-values, of conditional DGP, of the conditional mean of xt given the past values of x and y, and, more generally, the conditional mean of (xt, yt) given their past values (vector autoregression). We establish, among other results, the central limit theorems for these estimators under far weaker mixing conditions than those used in Robinson [23], where only the xt series is considered. Uniform consistency and rate results for the consistencies of various estimators are also obtained. The results of the paper are useful in light of the fact that often the functional form of the dynamic regression is not known and also the assumption of the Gaussian process is not true.
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Suggested Citation

  • Radhey S. Singh & Aman Ullah, 1984. "Nonparametric Time Series Estimation of Joint DGP, Conditional DGP and Vector Autoregression," University of Western Ontario, Departmental Research Report Series 8423, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:8423
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    Cited by:

    1. Wu, Wei Biao & Huang, Yinxiao & Huang, Yibi, 2010. "Kernel estimation for time series: An asymptotic theory," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2412-2431, December.
    2. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
    3. Baghli, Mustapha & Cahn, Christophe & Fraisse, Henri, 2007. "Is the inflation-output Nexus asymmetric in the Euro area?," Economics Letters, Elsevier, vol. 94(1), pages 1-6, January.
    4. Ghysels, E. & Ng, S., 1996. "A Semi-Parametric Factor Model for Interest Rates," Cahiers de recherche 9612, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    5. Pagan, Adrian & Ullah, Aman, 1988. "The Econometric Analysis of Models with Risk Terms," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(2), pages 87-105, April.
    6. John Knight & Fuchun Li & Mingwei Yuan, 2006. "A Semiparametric Two-Factor Term Structure Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 204-237.

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