Nonparametric approach for non-Gaussian vector stationary processes
Journal of Multivariate Analysis
Time series: data analysis and theory
Time series: data analysis and theory
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We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator @b@^ 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 @b@^. Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that @b@^ 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 @b@^. Numerical studies are given to confirm the theoretical results.