On open and controversial issue in empirical data analysis is to decide whether scaling and multifractal properties observed in empirical data actually exist, or whether they are induced by intricate non stationarities. To contribute to answering this question, we propose a procedure aiming at testing the constancy along time of multifractal attributes estimated over adjacent non overlapping time windows. The procedure is based on non parametric bootstrap resampling and on wavelet Leader estimations for the multifractal parameters. It is shown, by means of numerical simulations on synthetic multifractal processes, that the proposed procedure is reliable and powerful for discriminating true scaling behavior against non stationarities. We end up with a practical procedure that can be applied to a single finite length observation of data with unknown statistical properties.