A new test of stationarity and its application to teletraffic data

In this contribution we generalize the test of sphericity as a test of stationarity for time-series. The sphericity statistics is in our case a measure of distance between the empirical correlations calculated on two contiguous segments of the same process. We prove that under the hypothesis of stationarity the logarithm of the sphericity converges in distribution to a quadratic form in a multidimensional gaussian random variable with a convergence rate that is equal to the length of the observation window. We then derive a test of proportionality of the correlations of the process on the two segments. This new test of stationarity is applied to test if the traffic measured on today's broadband networks is stationary. The results that we obtain are connected to many previous works according to which the traffic generated by modern high-speed networks is a stationary and long-range dependent process.