Sieve Inference on Semi-Nonparametric Time Series Models

55 Pages Posted: 21 Feb 2012

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics

Yixiao Sun

University of California, San Diego (UCSD) - Department of Economics

Date Written: February 21, 2012

Abstract

The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a "pre-asymptotic" sieve variance estimator that captures temporal dependence. We construct a "pre-asymptotic" Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled "pre-asymptotic" Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled "pre-asymptotic" Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values.

Keywords: Weak dependence, Sieve M estimation, Sieve Riesz representor, Irregular functional, Misspecification, Pre-asymptotic variance, Orthogonal series long run variance estimation, F distribution

JEL Classification: C12, C14, C32

Suggested Citation

Chen, Xiaohong and Liao, Zhipeng and Sun, Yixiao, Sieve Inference on Semi-Nonparametric Time Series Models (February 21, 2012). Cowles Foundation Discussion Paper No. 1849, Available at SSRN: https://ssrn.com/abstract=2008720 or http://dx.doi.org/10.2139/ssrn.2008720

Xiaohong Chen (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics ( email )

8283 Bunche Hall
Los Angeles, CA 90095-1477
United States

Yixiao Sun

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
858-534-4692 (Phone)
858-534-7040 (Fax)

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