Unit root testing in economic or financial time series data is an important precondition for further statistical analysis. It is widely employed in time series analysis to assess the stationarity properties of variables, with lag selection playing a critical role in test performance. However, the choice of lag selection method can significantly influence test statistics, power, and size distortions, leading to potential implications for empirical inference. This study conducts a comparative analysis of lag selection methods and their effects on the performance of unit root tests. The order of integration of long-term interest rates in 23 European countries was examined using augmented Dickey-Fuller (ADF) and generalized least squares Dickey-Fuller (DF-GLS) tests. We compared the rejection rate of the unit root hypothesis under different lag selection techniques. Of particular interest is influence of the choice of optimal lag-length on the outcome of stationarity tests with these two major methods. We provide empirical evidence that shows that the outcome of unit root test is crucially dependent on the appropriate choice of lag length. The findings offer insights into the relative merits and limitations of each method, contributing to methodological understanding in time series analysis. Practical implications for researchers are discussed, providing guidance for selecting appropriate lag selection methods in unit root testing and enhancing the reliability of empirical inference in nonstationary time series data analysis.