Staff Working Paper No. 721
By Ching-Wai (Jeremy) Chiu, Simon Hayes, George Kapetanios and Konstantinos Theodoridis
Forecasts play a critical role at inflation-targeting central banks, such as the Bank of England. Breaks in the forecast performance of a model can potentially incur important policy costs. Commonly used statistical procedures, however, implicitly put a lot of weight on type I errors (or false positives), which result in a relatively low power of tests to identify forecast breakdowns in small samples. We develop a procedure which aims at capturing the policy cost of missing a break. We use data-based rules to find the test size that optimally trades off the costs associated with false positives with those that can result from a break going undetected for too long. In so doing, we also explicitly study forecast errors as a multivariate system. The covariance between forecast errors for different series, though often overlooked in the forecasting literature, not only enables us to consider testing in a multivariate setting but also increases the test power. As a result, we can tailor the choice of the critical values for each series not only to the in-sample properties of each series but also to how the series for forecast errors covary.