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A new approach for detecting shifts in forecast accuracy
Institution:1. Bank of England, Threadneedle Street, London, EC2R 8AH, United Kingdom;2. Centre for Macroeconomics, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE, United Kingdom;1. University of Bristol, United Kingdom;2. Bank of England, United Kingdom;1. Bank of England and CEPR, UK;2. Bank of England and Centre for Macroeconomics, UK;3. Bank of England, London, UK
Abstract: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. However, commonly-used statistical procedures implicitly place a lot of weight on type I errors (or false positives), which results in a relatively low power of the tests to identify forecast breakdowns in small samples. We develop a procedure which aims to capture 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, although 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 our choice of the critical values for each series not only to the in-sample properties of each series, but also to the way in which the series of forecast errors covary.
Keywords:Forecast breaks  Statistical decision making  Optimal test sizes  Hypothesis testing with small sample sizes  Central banking
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