COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1849 Sieve Inference on Semi-nonparametric Time Series Models Xiaohong Chen, Zhipeng Liao and Yixiao Sun February 2012 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. |
