Structural stability is often tested by checking whether the coefficients of a regression model are constant across different sub-samples. Such tests are commonly used as a general specification test, based on the belief that a correctly specified model should have constant parameters (or ‘invariant’ parameters if some aspect of the economic regime or policy stance has changed). A related set of testing procedures is the focus of this chapter, where we wish to test whether a model estimated over one period can provide adequate forecasts over a subsequent period. Such tests are known as tests of predictive failure. Finally, we consider the problems inherent in directly comparing two sets of rival forecasts of the same phenomena independently of the models from which they were produced.