A note on testing hypotheses for stationary processes in the frequency domain
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Date
2010-05-03T14:21:27Z
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Abstract
In a recent paper Eichler (2008) considered a class of non- and semiparametric hypotheses in multivariate stationary processes, which are characterized by a functional of the spectral density
matrix. The corresponding statistics are obtained using kernel estimates for the spectral distribution and are asymptotically normal distributed under the null hypothesis and local alternatives. In this paper we derive the asymptotic properties of these test statistics under fixed alternatives. In
particular we show also weak convergence but with a different rate compared to the null hypothesis.
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Keywords
Goodness-of-fit test, Kernel estimate, Smoothed periodogram, Stationary process, Weak convergence under the alternative