Article thumbnail
Location of Repository

Efficient Regression in Time Series Partial Linear Models

By Peter C.B. Phillips, Binbin Guo and Zhijie Xiao


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.Efficient estimation, Partial linear regression, Spectral regression, Kernel estimation, Nonparametric, Semiparametric, Weak dependence

OAI identifier:

Suggested articles


  1. (1971). A General Approximation to the Distribution of Instrumental Variables Estimates,
  2. (1977). A General Theorem in the Theory of Asymptotic Expansion As Approximations to the Finite Sample Distributions of Econometric Estimators,
  3. (1994). A Reexamination of the consumption Function Using Frequency Domain Regressions,
  4. (1991). Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models,
  5. (1974). Band spectrum regression,
  6. (1986). Convergence rate for partially linear splined models,
  7. (1988). Convergence Rates for Parametric Components in a Partial Linear Model,” The Annals of Statistics,
  8. (1976). Econometric Estimators and the Edgeworth Expansion,
  9. (1998). Higher Order approximations for frequency domain time series regression”,
  10. (1988). Kernel Smoothing in Partial Linear Models”,
  11. M(1988), Root-n-consistent semiparametric regression,
  12. (1970). Multiple Time Series.N e wY o r k :W i l e y .
  13. (1971). Nonlinear Time Series Regression,
  14. (1986). On asymptotically efficient estimation in semiparametric models,
  15. (1984). Partial spline models for the semiparametric estimation of functions of several variables, in Statistical analysis of Time series,T o k y o :I n -stitute of Statistical Mathematics,
  16. (2000). Partially Linear Models with Unit Roots, Working paper,
  17. (1963). Regression for Time Series with
  18. (1999). Root-N-Consistent Estimation of Partially Linear Time Series Models,”
  19. (1995). Second Order Approximation in a Linear Regression with Heteroskedasticity of Unknown Form,
  20. (1995). Second Order Approximation in the Partially Linear Regression Model,
  21. (1986). Semiparametric estimates for the relation between weather and electricity demand,
  22. (1985). Semiparametric generalized linear models,”
  23. Smoothness priors and nonlinear regression,
  24. (1981). Spectral Analysis and Time Series,
  25. (1986). Spline smoothing in apartial linear model,
  26. (1980). Time Series: Data Analysis and Theory.N e wY o r k : Holt, Rinehart and Winston.
  27. (2000). Unit Root Log Periodogram Regression. Cowles Foundation Discussion Paper #

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.