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Second order optimality for estimators in time series regression models

  • Tamaki, Kenichiro
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    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.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 3 (March)
    Pages: 638-659

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:638-659
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    1. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(03), pages 497-539, June.
    2. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
    3. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    4. Xiao, Zhijie & Phillips, Peter C. B., 2002. "Higher order approximations for Wald statistics in time series regressions with integrated processes," Journal of Econometrics, Elsevier, vol. 108(1), pages 157-198, May.
    5. Xiao, Zhijie & Phillips, Peter C. B., 1998. "Higher-order approximations for frequency domain time series regression," Journal of Econometrics, Elsevier, vol. 86(2), pages 297-336, June.
    6. Taniguchi, Masanobu & van Garderen, Kees Jan & Puri, Madan L., 2003. "Higher Order Asymptotic Theory For Minimum Contrast Estimators Of Spectral Parameters Of Stationary Processes," Econometric Theory, Cambridge University Press, vol. 19(06), pages 984-1007, December.
    7. Toyooka, Yasuyuki, 1985. "Second-order risk comparison of SLSE with GLSE and MLE in a regression with serial correlation," Journal of Multivariate Analysis, Elsevier, vol. 17(2), pages 107-126, October.
    8. Oliver Linton & Zhijie Xiao, 2001. "Second-order approximation for adaptive regression estimators," LSE Research Online Documents on Economics 317, London School of Economics and Political Science, LSE Library.
    9. Rothenberg, Thomas J, 1984. "Approximate Normality of Generalized Least Squares Estimates," Econometrica, Econometric Society, vol. 52(4), pages 811-25, July.
    10. Taniguchi, Masanobu & Puri, Madan L. & Kondo, Masao, 1996. "Nonparametric Approach for Non-Gaussian Vector Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 259-283, February.
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