Economic data are collected at various frequencies but econometric estimation typically uses the coarsest frequency. This paper develops a Gibbs sampler for estimating VAR models with mixed and irregularly sampled data. The Gibbs sampler allows efficient likelihood inference and uses simple conjugate posteriors even in high dimensional parameter spaces, avoiding a non-Gaussian likelihood surface even when the Kalman filter applies. Two examples studying the relationship between financial data and the real economy illustrate the methodology and demonstrates efficiency gains from the mixed frequency estimator.

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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.