Censored Density Forecasts: Production and Evaluation

81 Pages Posted: 1 Jun 2021 Last revised: 17 Aug 2022

See all articles by James Mitchell

James Mitchell

Federal Reserve Bank of Cleveland

Martin Weale

King’s College London

Date Written: August 16, 2022

Abstract

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 find that these outperform the official forecasts produced by the MPC.

Keywords: Forecast uncertainty, Outliers, Fan charts, Skewed densities, Best critical region, Density forecasting, Censoring, Forecast evaluation

JEL Classification: C24, C46, C53, E58

Suggested Citation

Mitchell, James and Weale, Martin, Censored Density Forecasts: Production and Evaluation (August 16, 2022). FRB of Cleveland Working Paper No. 21-12R, Available at SSRN: https://ssrn.com/abstract=3854952 or http://dx.doi.org/10.2139/ssrn.3854952

James Mitchell (Contact Author)

Federal Reserve Bank of Cleveland ( email )

East 6th & Superior
Cleveland, OH 44101-1387
United States

HOME PAGE: http://https://www.clevelandfed.org/en/our-research/economists/james-mitchell.aspx

Martin Weale

King’s College London ( email )

Strand
London, England WC2R 2LS
United Kingdom

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