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Second order optimality for estimators in time series regression models

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  • Tamaki, Kenichiro

Abstract

We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator 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 . Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that 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 . Numerical studies are given to confirm the theoretical results.

Suggested Citation

  • Tamaki, Kenichiro, 2007. "Second order optimality for estimators in time series regression models," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 638-659, March.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:638-659
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    Cited by:

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    2. Daniel Wilhelm, 2014. "Optimal bandwidth selection for robust generalized method of moments estimation," CeMMAP working papers 15/14, Institute for Fiscal Studies.

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