Second order optimality for estimators in time series regression models

  • Tamaki K
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Abstract

We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator over(β, ^) proposed by Hannan [Regression for time series, Proc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963, pp. 17-37]. This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of over(β, ^). Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that over(β, ^) 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 over(β, ^). Numerical studies are given to confirm the theoretical results. © 2006 Elsevier Inc. All r ights reserved.

Author-supplied keywords

  • efficient estimation
  • second order asymptotics
  • semiparametric estimation
  • spectral regression

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  • K Tamaki

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