Testing nonstationary time series for Gaussianity and linearity using the evolutionary bispectrum: An application to internet traffic data

We propose statistical tests for Gaussianity and linearity of nonstationary time series based on the evolutionary bispectrum. These tests can be applied to a particular subclass of nonstationary processes, the so-called oscillatory or slowly varying. We run some simulated examples and examine the power of the tests. Then we apply these tests to time series of network measurements arising from internet traffic, processes which have been demonstrated by several researchers to be typically nonstationary. We also address the question of whether such processes can be described by some model whose parameters vary with time. We show that there is evidence of non-Gaussianity and nonlinearity in such processes under the assumption that they are described by a model whose parameters (and so its spectral characteristics) vary slowly with time.