Second order optimality for estimators in time series regression models

Abstract

We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimatorˆ proposed by Hannan [Regression for time series, Proc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963. This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of . Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies thatˆ has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency ofˆ . Numerical studies are given to confirm the theoretical results.

Optimal Bandwidth Selection for Robust Generalized Method of Moments Estimation

“…Robinson (1991), Xiao and Phillips (1998) and Tamaki (2007)) that derive higher-order expansions of the MSE of semiparametric frequency domain estimators to determine an optimal bandwidth that minimizes higher-order terms of such expansions. In the present paper, however, we allow for nonlinear models and over-identification which significantly complicate the problem and require a different set of tools to derive such expansions.…”