Unit root testing is an important procedure when performing time series analysis, since all the succeeding inferences should be performed based on a stationary series. Thus, it is crucial to test the stationarity of the time series in hand accurately and efficiently. One issue among the existing popular unit root testing methods is that they all require certain assumptions about the model specification, whether on the functional form or the stochastic term distribution; then all the analyses are performed based on the pre-determined model. However, various circumstances such as data incompleteness, variable selection, and distribution misspecification which may lead to an inappropriate model specification that will produce an erroneous conclusion since the test result depends on the particular model considered. This dissertation focuses on confronting this issue by proposing a new numerical Bayesian unit root test incorporating model averaging which can take model uncertainty as well as variable transformation into account. The first chapter introduces a broad literature review of all the building blocks need for the development of the new methods, including traditional frequentist unit root tests, Bayesian unit root tests, and Bayesian model averaging. Following chapter II elaborates the mathematical derivation of the proposed methods, Monte Carlo simulation study and results, as well as testing conclusions on the benchmark Nelson and Plosser (1982) macroeconomic time series. Chapter III applies the method to investigate the effect of data frequency on unit root test results particularly for financial data. We perform our proposed Bayesian Model Averaging method to five commodity futures price series by averaging GARCH and ARCH models with different mean functions and distribution specifications to demonstrate the robustness and usefulness of our method especially when model specification uncertainty issue is presented. Overall, the proposed numerical Bayesian unit root test is a general approach to considering model uncertainty when performing the stationary tests, and it provides an alternative to researchers who are concerned this is a significant issue in their research.