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Testing for cycles in multiple time series
Author(s) -
Ploberger Werner,
Reschenhofer Erhard
Publication year - 2010
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.1467-9892.2010.00675.x
Subject(s) - mathematics , smoothness , series (stratigraphy) , harmonics , gravitational singularity , bayesian probability , spectrum (functional analysis) , spectral density , statistics , statistical hypothesis testing , econometrics , mathematical analysis , paleontology , physics , quantum mechanics , voltage , biology
In practice, it is often impossible to assess the validity of the smoothness assumptions crucial to standard tests for singularities in the spectrum. We therefore propose new tests which are completely insensitive to sharp peaks in the absolutely continuous part of the spectrum. Using Neyman Pearson tests of Bayesian mixtures we first derive admissible tests under simplifying assumptions and then show that under realistic assumptions our test statistics remain the same. The tests are designed to have high power especially against alternatives containing oscillations which are positively correlated with each other. Motivated by a biological dataset with non‐sinusoidal oscillations, we finally extend our approach by including higher harmonics.