Nonparametric Transformation to White Noise

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Nonparametric Transformation to White Noise

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Oliver Linton
Enno Mammen

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Abstract

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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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

This paper has been announced in the following NEP Reports:

NEP-ALL-2006-10-28 (All new papers)
NEP-ECM-2006-10-28 (Econometrics)
NEP-ETS-2006-10-28 (Econometric Time Series)

References listed on IDEAS
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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. [Downloadable!] (restricted)
Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation, Yale University. [Downloadable!]
Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
Other versions:
- Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation, Yale University, revised Feb 1986. [Downloadable!]
Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-63, May. [Downloadable!] (restricted)
Geweke, John F, 1978. "Temporal Aggregation in the Multiple Regression Model," Econometrica, Econometric Society, vol. 46(3), pages 643-61, May. [Downloadable!] (restricted)
Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November. [Downloadable!] (restricted)
Oliver Linton & Enno Mammen, 2003. "Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods," STICERD - Econometrics Paper Series /2003/453, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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. [Downloadable!] (restricted)
W. H"Ardle & O. Linton, . "Nonparametric Regression," Sonderforschungsbereich 373 1995-29, Humboldt Universitaet Berlin.

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Gregory Connor & Matthias Hagmann & Oliver Linton, 2007. "Efficient Estimation of a SemiparametricCharacteristic-Based Factor Model of Security Returns," STICERD - Econometrics Paper Series /2007/524, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]

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