A note on testing hypotheses for stationary processes in the frequency domain

作者：Dette Holger^*; Hildebrandt Thimo

来源：Journal of Multivariate Analysis, 2012, 104(1): 101-114.

DOI：10.1016/j.jmva.2011.07.002

• Stationary process
• Goodness-of-fit tests
• Kernel estimate
• Smoothed periodogram
• Weak convergence under the alternative

In a recent paper, Eichler (2008) [11] 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 normally 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 also show weak convergence but with a different rate compared to the null hypothesis. We also discuss potential statistical applications of the asymptotic theory by means of a small simulation study.

• 出版日期2012-2