Evaluating, Comparing and Combining Density Forecasts Using the KLIC with an Application to the Bank of England and NIESR ‘Fan’ Charts of Inflation†

  1. James Mitchell1,
  2. Stephen G. Hall1,2

Article first published online: 6 DEC 2005

DOI: 10.1111/j.1468-0084.2005.00149.x

Issue

Oxford Bulletin of Economics and Statistics

Oxford Bulletin of Economics and Statistics

Volume 67, Issue Supplement s1, pages 995–1033, December 2005

Additional Information

How to Cite

Mitchell, J. and Hall, S. G. (2005), Evaluating, Comparing and Combining Density Forecasts Using the KLIC with an Application to the Bank of England and NIESR ‘Fan’ Charts of Inflation. Oxford Bulletin of Economics and Statistics, 67: 995–1033. doi: 10.1111/j.1468-0084.2005.00149.x

Author Information

  1. 1

    National Institute of Economic and Social Research (NIESR), London, UK (e-mail: j.mitchell@niesr.ac.uk)

  2. 2

    Department of Economics, Leicester University, Leicester, UK (e-mail: s.g.hall@leicester.ac.uk)

  • †

    We would like to thank two anonymous referees for helpful comments. Particular thanks to Kenneth Wallis for comments on an earlier related paper that have also helped us develop our ideas in this paper. Mitchell gratefully acknowledges financial support from the ESRC (Award Reference: RES-000-22-0610). All errors remain our own.

Publication History

  1. Issue published online: 6 DEC 2005
  2. Article first published online: 6 DEC 2005

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Keywords:

  • C53;
  • E37

Abstract

This paper proposes and analyses the Kullback–Leibler information criterion (KLIC) as a unified statistical tool to evaluate, compare and combine density forecasts. Use of the KLIC is particularly attractive, as well as operationally convenient, given its equivalence with the widely used Berkowitz likelihood ratio test for the evaluation of individual density forecasts that exploits the probability integral transforms. Parallels with the comparison and combination of point forecasts are made. This and related Monte Carlo experiments help draw out properties of combined density forecasts. We illustrate the uses of the KLIC in an application to two widely used published density forecasts for UK inflation, namely the Bank of England and NIESR ‘fan’ charts.

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