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Nonparametric Transformation to White Noise

  • Oliver Linton
  • Enno Mammen

We consider a semiparametric distributed lag model in which the "news impact curve" m isnonparametric but the response is dynamic through some linear filters. A special case ofthis is a nonparametric regression with serially correlated errors. We propose an estimatorof the news impact curve based on a dynamic transformation that produces white noiseerrors. This yields an estimating equation for m that is a type two linear integral equation.We investigate both the stationary case and the case where the error has a unit root. In thestationary case we establish the pointwise asymptotic normality. In the special case of anonparametric regression subject to time series errors our estimator achieves efficiencyimprovements over the usual estimators, see Xiao, Linton, Carroll, and Mammen (2003). Inthe unit root case our procedure is consistent and asymptotically normal unlike the standardregression smoother. We also present the distribution theory for the parameter estimates,which is non-standard in the unit root case. We also investigate its finite sampleperformance through simulation experiments.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2006/503.

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Date of creation: Aug 2006
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Handle: RePEc:cep:stiecm:/2006/503
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  1. Xiao Z. & Linton O.B. & Carroll R.J. & Mammen E., 2003. "More Efficient Local Polynomial Estimation in Nonparametric Regression With Autocorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 980-992, January.
  2. Geweke, John F, 1978. "Temporal Aggregation in the Multiple Regression Model," Econometrica, Econometric Society, vol. 46(3), pages 643-61, May.
  3. Oliver Linton & E. Mammen & J. Nielsen, 1999. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions," LSE Research Online Documents on Economics 300, London School of Economics and Political Science, LSE Library.
  4. Newey, W.K., 1989. "The Asymptotic Variance Of Semiparametric Estimotors," Papers 346, Princeton, Department of Economics - Econometric Research Program.
  5. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-63, May.
  6. Hendry, David F. & Pagan, Adrian R. & Sargan, J.Denis, 1984. "Dynamic specification," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 18, pages 1023-1100 Elsevier.
  7. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-53, October.
  8. Oliver Linton & Enno Mammen, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
  9. Zudi Lu, 2001. "Asymptotic Normality of Kernel Density Estimators under Dependence," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(3), pages 447-468, September.
  10. 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.
  11. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  12. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, 05.
  13. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
  14. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-77.
  15. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
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