Test to compare two population logspectra

The objective of this paper is to compare time series patterns generated over two populations. A random sample of objects is chosen from each population. On each object, a stationary process with an absolutely continuous spectral distribution is observed at the same times. We assume that the logarithm of the periodogram from each time series follows a model which involves the pattern of each population. A statistical test is proposed which will compare these patterns. The probability distribution of the test under the null hypothesis is approximated by the bootstrap. The consistency of the method is analyzed using the Mallows metric. A simulation study is also carried out.