Nonparametric transformation to white noise
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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