Censored Density Forecasts: Production and Evaluation

This paper develops methods for the production and evaluation of censored density forecasts. Censored density forecasts quantify forecast risks in a middle region of the density covering a specified probability, and ignore the magnitude but not the frequency of outlying observations. We propose a new estimator that fits a potentially skewed and fat-tailed density to the inner observations, acknowledging that the outlying observations may be drawn from a different but unknown distribution. We also introduce a new test for calibration of censored density forecasts. An application using historical forecast errors from the Federal Reserve Board and the Monetary Policy Committee at the Bank of England illustrates the utility of censored density forecasts when quantifying forecast risks after shocks such as the global financial crisis and the COVID-19 pandemic.