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Sieve inference on semi-nonparametric time series models

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  • Xiaohong Chen
  • . .
  • Yixiao Sun

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.

Suggested Citation

  • Xiaohong Chen & . . & Yixiao Sun, 2012. "Sieve inference on semi-nonparametric time series models," CeMMAP working papers 06/12, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:06/12
    DOI: 10.1920/wp.cem.2012.0612
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    References listed on IDEAS

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