Sieve Inference on Semi-nonparametric Time Series Models

Xiaohong Chen (), Zhipeng Liao and Yixiao Sun

No 1849, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 (search for similar items in EconPapers)
JEL-codes: C12 C14 C32 (search for similar items in EconPapers)
Pages: 54 pages
Date: 2012-02
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: CFP 1401
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Published in Journal of Econometrics (January 2014), 178(3): 639-658

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Working Paper: Sieve inference on semi-nonparametric time series models (2012)
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