Break Detectability and Mean Square Forecast Error Ratios for Selecting Estimation Windows

It has been suggested that a major problem for window selection when we estimate models for forecasting is to empirically determine the timing of the break. However, if the window choice between post‐break or full sample is based on mean square forecast error ratios, it is difficult to understand why such a problem arises since break detectability and these ratios seem to have the same determinants. This paper analyses this issue first for the expected values in conditional models and then by Monte Carlo simulations for more general cases. Results show similar behaviour between rejection frequencies and the ratios but only for break tests that do not take into account forecasting error covariances, as is the case with mean square forecast error measures. Moreover, the asymmetric shape of the frequency distribution of the ratios could help us to better grasp empirical problems. An illustration using actual data is given. Copyright © 2011 John Wiley & Sons, Ltd.