Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/64726 
Year of Publication: 
2012
Series/Report no.: 
cemmap working paper No. CWP06/12
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
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.
Subjects: 
Weak Dependence
Sieve M Estimation
Sieve Riesz Representor
Irregular Functional
Misspecification
Pre-asymptotic Variance
Orthogonal Series Long Run Variance Estimation
F Distribution
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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