Second order optimality for estimators in time series regression models

摘要

We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator (beta) over tilde proposed by Hannan I Regression for time series, Proc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963, pp. 17-371. This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of (beta) over tilde. Then it is shown that the second order asymtotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that (beta) over tilde 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 of (beta) over tilde Numerical studies are given to confirm the theoretical results. (c) 2006 Elsevier Inc. All rights reserved.