This article provides a comparative analysis of mathematical and statistical methods used in the framework of the Turkish scientific literature devoted to the study of the information efficiency of the Turkish stock market. It is shown that the majority of research on this topic is conducted in a paradigm that identifies the random walk with the presence of unit roots in time series. It is proved that this approach is not strict enough and, in many cases, leads to false acceptance of the information efficiency hypothesis. It is shown for the first time that such popular methods as the Augmented Dickey-Fuller test or the Kapetanios-Snell-Shin test, which allow to find unit roots, have limited applicability in the framework of studying the information efficiency. There are listed the most common mistakes that are often made when using these tests. There are also indicated some methods (in particular, fractal methods) that, in the opinion of the authors, are more applicable and deserve more frequent use. It is pointed out and proven that switching attention from the search for unit roots to the study of time series variation will keep the random walk paradigm and, at the same time, will advance the study of the information efficiency. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.