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Expansion of Brownian Motion Functionals and Its Application in Econometric Estimation

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Listed:
  • Chaohua Dong
  • Jiti Gao

Abstract

Two types of Brownian motion functionals, both time-homogeneous and time-inhomogeneous, are expanded in terms of orthonormal bases in respective Hilbert spaces. Meanwhile, different time horizons are treated from the applicability point of view. Moreover, the degrees of approximation of truncation series to the corresponding series are established. An asymptotic theory is established. Both the proposed expansions and asymptotic theory are applied to establish consistent estimators in a class of time series econometric models.

Suggested Citation

  • Chaohua Dong & Jiti Gao, 2011. "Expansion of Brownian Motion Functionals and Its Application in Econometric Estimation," Monash Econometrics and Business Statistics Working Papers 19/11, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2011-19
    as

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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp19-11.pdf
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    References listed on IDEAS

    as
    1. Jiti Gao & Peter C. B. Phillips, 2010. "Semiparametric Estimation in Time Series of Simultaneous Equations," Cowles Foundation Discussion Papers 1769, Cowles Foundation for Research in Economics, Yale University.
    2. Wolfgang Hardle & Helmut Herwartz & Vladimir Spokoiny, 2003. "Time Inhomogeneous Multiple Volatility Modeling," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 55-95.
    3. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1466-1497, December.
    4. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    5. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    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. Bandi, Federico M. & Phillips, Peter C.B., 2007. "A simple approach to the parametric estimation of potentially nonstationary diffusions," Journal of Econometrics, Elsevier, vol. 137(2), pages 354-395, April.
    8. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    9. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    10. Hansen, Lars Peter & Sargent, Thomas J, 1983. "The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities," Econometrica, Econometric Society, vol. 51(2), pages 377-387, March.
    11. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
    12. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    14. Jiti Gao & Peter C. B. Phillips, 2010. "Semiparametric Estimation in Simultaneous Equations of Time Series Models," School of Economics and Public Policy Working Papers 2010-26, University of Adelaide, School of Economics and Public Policy.
    15. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    16. Phillips, P. C. B., 1973. "The problem of identification in finite parameter continuous time models," Journal of Econometrics, Elsevier, vol. 1(4), pages 351-362, December.
    17. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Asymptotic theory; Brownian motion; econometric estimation; series expansion.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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