The unit root revolution in time series modeling has created substantial interest in non- stationarity and its implications for empirical modeling. Beyond the original interest in trend vs. di¤erence non-stationarity, there has been renewed interest in testing and modeling structural breaks. The focus of my dissertation is on testing for departures from stationarity in a broader framework where unit root, mean trends and structural break non-stationarity constitute only a small subset of the possible forms of non-stationarity. In the fi¦rst chapter the most popular testing procedures for the assumption, in view of the fact that general forms of non-stationarity render each observation unique, I develop a testing procedure using a resampling scheme which is based on a Maximum Entropy replication algorithm. The proposed misspecification testing procedure relies on resampling techniques to enhance the informational content of the observed data in an attempt to capture heterogeneity 'locally' using rolling window estimators of the primary moments of the stochastic process. This provides an e¤ective way to enhance the sample information in order to assess the presence of departures from stationarity. Depending on the sample size, the method utilizes overlapping or non-overlapping window estimates. The e¤ectiveness of the testing procedure is assessed using extensive Monte Carlo simulations. The use of rolling non-overlapping windows improves the method by improving both the size and power of the test. In particular, the new test has empirical size very close to the nominal and very high power for a variety of departures from stationarity. The proposed procedure is then applied on seven macroeconomic series in the fourth chapter. Finally, the optimal choice of orthogonal polynomials, for hypothesis testing, is investigated in the last chapter. / Ph. D.