Comparing non-stationary and irregularly spaced time series

In this paper we present approximate distributions for the ratio of the cumulative wavelet periodograms considering stationary and non-stationary time series generated from independent Gaussian processes. We also adapt an existing procedure to use this statistic and its approximate distribution in order to test if two regularly or irregularly spaced time series are realizations of the same generating process. Simulation studies show good size and power properties for the test statistic. An application with financial microdata illustrate the test usefulness. We conclude advocating the use of these approximate distributions instead of the ones obtained trough randomizations, mainly in the case of irregular time series.