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Efficient estimation of forecast uncertainty based on recent forecast errors

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  • Knüppel, Malte

Abstract

Multi-step-ahead forecasts of forecast uncertainty in practice are often based on the horizon-specific sample means of recent squared forecast errors, where the number of available past forecast errors decreases one-to-one with the forecast horizon. In this paper, the efficiency gains from the joint estimation of forecast uncertainty for all horizons in such samples are investigated. Considering optimal forecasts, the efficiency gains can be substantial if the sample is not too large. If forecast uncertainty is estimated by seemingly unrelated regressions, the covariance matrix of the squared forecast errors does not have to be estimated, but simply needs to have a certain structure. In Monte Carlo studies it is found that seemingly unrelated regressions mostly yield estimates which are more efficient than the sample means even if the forecasts are not optimal. Seemingly unrelated regressions are used to address questions concerning the inflation forecast uncertainty of the Bank of England. --

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Bibliographic Info

Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2009,28.

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Date of creation: 2009
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Handle: RePEc:zbw:bubdp1:200928

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Keywords: Multi-step-ahead forecasts; forecast error variance; GLS; SUR;

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  1. Kajal Lahiri & Fushang Liu, 2006. "Modeling Multi-Period Inflation Uncertainty Using a Panel of Density Forcasts," Discussion Papers 06-05, University at Albany, SUNY, Department of Economics.
  2. Giordani, Paolo & Soderlind, Paul, 2003. "Inflation forecast uncertainty," European Economic Review, Elsevier, vol. 47(6), pages 1037-1059, December.
  3. Kajal Lahiri & Xuguang Sheng, 2008. "Measuring Forecast Uncertainty by Disagreement: The Missing Link," Ifo Working Paper Series Ifo Working Paper No. 60, Ifo Institute for Economic Research at the University of Munich.
  4. Zarnowitz, Victor & Lambros, Louis A, 1987. "Consensus and Uncertainty in Economic Prediction," Journal of Political Economy, University of Chicago Press, vol. 95(3), pages 591-621, June.
  5. Knüppel, Malte, 2009. "Efficient estimation of forecast uncertainty based on recent forecast errors," Discussion Paper Series 1: Economic Studies 2009,28, Deutsche Bundesbank, Research Centre.
  6. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809, October.
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  8. Makridakis, Spyros & Hogarth, Robin M. & Gaba, Anil, 2009. "Forecasting and uncertainty in the economic and business world," International Journal of Forecasting, Elsevier, vol. 25(4), pages 794-812, October.
  9. David Reifschneider & Peter Tulip, 2007. "Gauging the uncertainty of the economic outlook from historical forecasting errors," Finance and Economics Discussion Series 2007-60, Board of Governors of the Federal Reserve System (U.S.).
  10. Wallis, Kenneth F, 1989. "Macroeconomic Forecasting: A Survey," Economic Journal, Royal Economic Society, vol. 99(394), pages 28-61, March.
  11. Zarnowitz, Victor, 1985. "Rational Expectations and Macroeconomic Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(4), pages 293-311, October.
  12. Brown, Bryan W & Maital, Shlomo, 1981. "What Do Economists Know? An Empirical Study of Experts' Expectations," Econometrica, Econometric Society, vol. 49(2), pages 491-504, March.
  13. Im, Eric Iksoon, 1994. "Unequal numbers of observations and partial efficiency gain," Economics Letters, Elsevier, vol. 46(4), pages 291-294, December.
  14. Victor Zarnowitz & Louis A. Lambros, 1983. "Consensus and Uncertainty in Economic Prediction," NBER Working Papers 1171, National Bureau of Economic Research, Inc.
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  1. Knüppel, Malte, 2009. "Efficient estimation of forecast uncertainty based on recent forecast errors," Discussion Paper Series 1: Economic Studies 2009,28, Deutsche Bundesbank, Research Centre.

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