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Expansion of Brownian Motion Functionals and Its Application in Econometric Estimation

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  • 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
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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
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    More about this item

    Keywords

    Asymptotic theory; Brownian motion; econometric estimation; series expansion.;

    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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