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Expansion of Brownian Motion Functionals and Its Application in Econometric Estimation

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  • Chaohua Dong
  • Jiti Gao

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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.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp19-11.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 19/11.

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Length: 60 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-19

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

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  1. Lars Peter Hansen & Thomas J. Sargent, 1981. "The dimensionality of the aliasing problem in models with rational spectral densities," Staff Report 72, Federal Reserve Bank of Minneapolis.
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  7. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
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  10. Federico M. Bandi & Peter C.B. Phillips, 2005. "A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions," Cowles Foundation Discussion Papers 1522, Cowles Foundation for Research in Economics, Yale University.
  11. Jiti Gao & Peter C. B. Phillips, 2010. "Semiparametric Estimation in Simultaneous Equations of Time Series Models," School of Economics Working Papers 2010-26, University of Adelaide, School of Economics.
  12. 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.
  13. 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.
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