Testing for Nonstationarity Using Maximum Entropy Resampling: A Misspecification Testing Perspective

One of the most important assumptions in empirical modeling is the constancy of the statistical model parameters which usually reflects the stationarity of the underlying stochastic process. In the 1980s and 1990s, the issue of nonstationarity in economic time series has been discussed in the context of unit roots vs. mean trends in AR(p) models. This perspective was subsequently extended to include structural breaks. In this article we take a much broader perspective by allowing for more general forms of nonstationarity. The focus of the article is primarily on misspecification testing. The proposed test relies on Maximum Entropy (ME) resampling techniques to enhance the information in the data in an attempt to capture heterogeneity “locally” using rolling window estimators. The t-heterogeneity of the primary moments of the process is generically captured using orthogonal Bernstein polynomials. The effectiveness of the testing procedure is assessed using Monte Carlo simulations.