Over the last two decades long memory time series have become an established modeling tool in many areas of science and technology, including geosciences, medical sciences, telecommunication networks and to some extend financial econometrics. It has however been recently realized that practically all statistical procedures intended to detect and estimate long memory give spurious results if a time series without long memory is perturbed by nonstationarities, like trends or breaks (change-points). For example, if a mean of a short memory time series changes, a test for the presence of long memory will incorrectly indicate that the time series has long memory. Similarly, a test for the presence of change point, will incorectly show that that a change point is present if the time series is stationary with long memory. A growing body of research which has accumulated over the last decade is concerned with finding and illustrating cases of such spurious inference, without addressing the issue how to choose between the two modeling approaches. In this talk we will discuss two new statistical tests aimed at distinguishing between the two approaches and apply them to a financial and a hydrological time series. The talk will focus on the ideas rather than technicalities and will be broadly accessible.