Second order optimality for estimators in time series regression models

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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.

Original languageEnglish
Pages (from-to)638-659
Number of pages22
JournalJournal of Multivariate Analysis
Volume98
Issue number3
DOIs
Publication statusPublished - 2007 Mar 1

Keywords

  • Efficient estimation
  • Second order asymptotics
  • Semiparametric estimation
  • Spectral regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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