The main purpose of this paper is to compare outcomes of the mentioned VR test for the evaluation of the RWH in 22 equity markets. Secondly, is to ascertain any changes in the random walk patterns of stock prices at the ten emerging markets, taking into account significant crises with the VR tests of Wright (2000) through a rolling window. The findings support that Wright's rank and sign and Whang-Kim's subsampling VR tests yield statistical results, which are less ambiguous as compared to the initial VR tests. That is clearer for relatively small sample sizes. Moreover, Chapter 2 presents the concept of "Efficient Market 1 hypothesis", while section 3 provides the theory and the features of the "Random Walk Hypothesis". Section 4 reports in detail the most important VR tests, including past similar studies. Last but not least, chapter 5 discusses the empirical results of every single test and depicts them with a pivot table.