Confidence intervals and statistical tests of spectral estimates of time series by using computer intensive methods

One of the tasks of spectral estimation is the detection of periodicities (signal) hidden in noise. Several statistical tests have been developed for the different methods of spectral estimation. For some estimators, like maximum entropy, the evaluation of the uncertainty of the estimates is usually difficult and generally based on distributional assumptions. A method is proposed in this study that is non-parametric and can be used assuming underlying white or red noise. The price to pay is that the method is computer intensive. Particularly, the proposed method is a Monte Carlo method based on random permutations of the original sample. The method may be applied to any spectral estimator and does not require any distributional assumptions. The procedure is illustrated with different examples and the results compared with parametric tests.