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Working Paper

Censored Density Forecasts: Production and Evaluation

This paper develops methods for the production and evaluation of censored density forecasts. The focus is on censored density forecasts that 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 fixed-point algorithm 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 (MPC) at the Bank of England suggests that the use of censored density functions to represent the pattern of forecast errors results in much greater parameter stability than do uncensored densities. We illustrate the utility of censored density forecasts when quantifying forecast risks after shocks such as the global financial crisis and the COVID-19 pandemic and and that these outperform the official forecasts produced by the MPC.

Working Papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views expressed in this paper are those of the authors and do not represent the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System.

Suggested Citation

Mitchell, James, and Martin Weale. 2022. “Censored Density Forecasts: Production and Evaluation.” Federal Reserve Bank of Cleveland, Working Paper No. 21-12R.