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Efficient Regression in Time Series Partial Linear Models

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Abstract

This paper studies efficient estimation of partial linear regression in time series models. In particular, it combines two topics that have attracted a good deal of attention in econometrics, viz. spectral regression and partial linear regression, and proposes an efficient frequency domain estimator for partial linear models with serially correlated residuals. A nonparametric treatment of regression errors is permitted so that it is not necessary to be explicit about the dynamic specification of the errors other than to assume stationarity. A new concept of weak dependence is introduced based on regularity conditions on the joint density. Under these and some other regularity conditions, it is shown that the spectral estimator is root-n-consistent, asymptotically normal, and asymptotically efficient.

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File URL: http://cowles.econ.yale.edu/P/cd/d13b/d1363.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1363.

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Length: 46 pages
Date of creation: May 2002
Date of revision:
Handle: RePEc:cwl:cwldpp:1363

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Efficient estimation; Partial linear regression; Spectral regression; Kernel estimation; Nonparametric; Semiparametric; Weak dependence;

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References

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  1. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
  2. Ted Juhl & Zhijie Xiao, 2002. "Partially Linear Models with Unit Roots," Cowles Foundation Discussion Papers 1359, Cowles Foundation for Research in Economics, Yale University.
  3. Sargan, J D & Mikhail, W M, 1971. "A General Approximation to the Distribution of Instrumental Variables Estimates," Econometrica, Econometric Society, vol. 39(1), pages 131-69, January.
  4. Phillips, Peter C B, 1977. "A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators," Econometrica, Econometric Society, vol. 45(6), pages 1517-34, September.
  5. R. F. Engle, 1972. "Band Spectrum Regressions," Working papers 96, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Corbae, Dean & Ouliaris, Sam & Phillips, Peter C B, 1994. "A Reexamination of the Consumption Function Using Frequency Domain Regressions," Empirical Economics, Springer, vol. 19(4), pages 595-609.
  7. Oliver Linton, 1993. "Second Order Approximation in the Partially Linear Regression Model," Cowles Foundation Discussion Papers 1065, Cowles Foundation for Research in Economics, Yale University.
  8. Xiao, Zhijie & Phillips, Peter C. B., 1998. "Higher-order approximations for frequency domain time series regression," Journal of Econometrics, Elsevier, vol. 86(2), pages 297-336, June.
  9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  10. Robert J. Shiller, 1982. "Smoothness Priors and Nonlinear Regression," NBER Technical Working Papers 0025, National Bureau of Economic Research, Inc.
  11. Oliver Linton, 1997. "Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form," Cowles Foundation Discussion Papers 1151, Cowles Foundation for Research in Economics, Yale University.
  12. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-48, May.
  13. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
  14. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
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Cited by:
  1. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2004. "The MIDAS Touch: Mixed Data Sampling Regression Models," University of California at Los Angeles, Anderson Graduate School of Management qt9mf223rs, Anderson Graduate School of Management, UCLA.
  2. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "The MIDAS Touch: Mixed Data Sampling Regression Models," CIRANO Working Papers 2004s-20, CIRANO.

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