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Testing non‐parametric hypotheses for stationary processes by estimating minimal distances
Author(s) -
Dette Holger,
Kinsvater Tatjana,
Vetter Mathias
Publication year - 2011
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2010.00703.x
Subject(s) - mathematics , test statistic , smoothing , parametric statistics , series (stratigraphy) , matrix (chemical analysis) , statistical hypothesis testing , constant (computer programming) , limit (mathematics) , spectral power distribution , nonparametric statistics , statistics , mathematical analysis , paleontology , materials science , physics , computer science , optics , composite material , biology , programming language
In this article, new tests for non‐parametric hypotheses in stationary processes are proposed. Our approach is based on an estimate of the L 2 ‐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.