This article presents a new filter for state-space models based on Bellman's dynamic programming principle applied to the posterior mode. The proposed Bellman filter generalises the Kalman filter including its extended and iterated versions, while remaining equally inexpensive computationally....

We use Google search data with the aim of predicting unemployment, CPI and consumer confidence for the US, UK, Canada, Germany and Japan. Google search queries have previously proven valuable in predicting macroeconomic variables in an in-sample context. To our knowledge, the more challenging...