This study examines the stock market index values of OECD countries using traditional and current econometric methods to test the validity of the efficiency hypothesis in financial markets. The efficiency hypothesis is defined as stock exchange markets' inability to be predicted through modeling. The reason why prices cannot be predicted in efficient markets is that prices exhibit random walks. When examining the descriptive statistics of financial time series, they are generally known to not conform to normal distributions. Therefore, the use of unit root tests based on the assumption of normal distribution in a financial time series may lead to incorrect results. As such, the empirical part of the study uses unit root tests based on the residual augmented least squares (RALS) method alongside unit root tests based on the assumption of normal distribution. To test the efficiency hypothesis on the stock market index values of 19 OECD countries, the study uses the Lagrange multiplier (LM) unit root tests with one and two structural breaks and RALS-LM tests, which are unit root tests based on the RALS method. According to the results from the Schmidt and Phillips (SP), LM and RALS-LM tests, the residuals from the auxiliary regressions of the SP and LM unit root tests were observed to not show normal distributions. Therefore, the residuals related to the financial series under consideration have been shown to not support the normality assumption. Additionally, when examining whether the series shows a unit-rooted process the RALS-LM unit root tests reject, the unit root hypothesis for more country market indexes than the SP and LM unit root tests. In other words, the study has determined the market prices of the relevant countries to not be efficient. In this case, making investment decisions would be appropriate by taking into account the knowledge that investors can predict prices in inefficient markets and that prices cannot be predicted in efficient markets.