Nonparametric Lag Selection for Additive Models based on the Smooth Backfitting Estimator

Zheng-Feng Guo,Ying He,Lingyan Cao

doi:10.4236/tel.2011.12004

Zheng-Feng Guo, Ying He + Show 1 more

Open Access

https://doi.org/10.4236/tel.2011.12004

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Abstract

This paper proposes a nonparametric FPE-like procedure based on the smooth backfitting estimator when the additive structure is a priori known. This procedure can be expected to perform well because of its well-known finite sample performance of the smooth backfitting estimator. Consistency of our procedure is established under very general conditions, including heteroskedasticity.

Highlights

With the wide application of nonparametric techniques in the time series literature, many nonparametric lag selection criteria based on kernel smoothing methods have been proposed; such as nonparametric FPE (Tjostheim and Auestad, 1994 [1] and Tschernig and Yang, 2000 [2]) and cross validation(Cheng and Tong, 1992 [3])
Tschernig and Yang (2000) [2] show the asymptotic equivalence of cross validation and nonparametric FPE and the consistency of the latter procedure originally proposed by Tjotheim and Auestad (1994) [1]
Guo and Shintani (2011) [4] impose the additivity assumption and propose a consistent FPE-like lag selection procedure based on the marginal integration method by Linton and Nelson (1995) [5]

Summary

Introduction

With the wide application of nonparametric techniques in the time series literature, many nonparametric lag selection criteria based on kernel smoothing methods have been proposed; such as nonparametric FPE (Tjostheim and Auestad, 1994 [1] and Tschernig and Yang, 2000 [2]) and cross validation(Cheng and Tong, 1992 [3]). Tschernig and Yang (2000) [2] show the asymptotic equivalence of cross validation and nonparametric FPE and the consistency of the latter procedure originally proposed by Tjotheim and Auestad (1994) [1]. Guo and Shintani (2011) [4] impose the additivity assumption and propose a consistent FPE-like lag selection procedure based on the marginal integration method by Linton and Nelson (1995) [5]. As is discussed in the conclusion of Guo and Shintani (2011) [4], the better finite sample properties of the backfitting method over marginal integration have been reported in simulation studies (e.g., Sperlich, Linton and Hardle, 1999 [6]).

The Nonparametric FPE for Additive Models

Estimation and the Consistency of our Criterion

Conclusions