Testing non‐parametric hypotheses for stationary processes by estimating minimal distances |
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Authors: | Holger Dette Tatjana Kinsvater Mathias Vetter |
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Affiliation: | Ruhr‐Universit?t Bochum |
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Abstract: | In this article, new tests for non‐parametric hypotheses in stationary processes are proposed. Our approach is based on an estimate of the L2‐distance between the spectral density matrix and its best approximation under the null hypothesis. We explain the main idea in the problem of testing for a constant spectral density matrix and in the problem of comparing the spectral densities of several correlated stationary time series. The method is based on direct estimation of integrals of the spectral density matrix and does not require the specification of smoothing parameters. We show that the limit distribution of the proposed test statistic is normal and investigate the finite sample properties of the resulting tests by means of a small simulation study. |
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Keywords: | Spectral density stationary process goodness‐of‐fit tests L2‐distance integrated periodogram 62M15 62G10 |
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