We show that the most popular estimators of the self-similarity index --- the Hurst and the DFA exponents --- cannot give exact value of the estimated parameter in some cases. The goal of this paper is to provide a simple computer test by means of which origins of the self-similarity feature of a particular time series can be found. We demonstrate that the observed self-similarity can reflect a long-memory (fractional Brownian motion case) or infinite variance of the process' increments (Lévy \alpha -stable motion case).

PACS numbers: 87.17.--d, 87.22.--q, 05.40.+j