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Forecast Evaluations for Multiple Time Series: A Generalized Theil Decomposition

Listed author(s):
  • Wolfgang Polasek

    ()

    (Institute of Advanced Studies, Austria)

The mean square error (MSE) compares point forecasts or a location parameter of the forecasting distribution with actual observations by the quadratic loss criterion. This paper shows how the Theil decomposition of the MSE error into a bias, variance and noise component which was proposed for univariate time series can be used to evaluate and compare multiple time series forecasts. Thus, for multivariate time series the ordinary and the alternative Theil decomposition is applied to decompose the MSE matrix. As an alternative we propose the average predictive ordinate criterion (APOC) which evaluates the ordinates of the predictive distribution for comparing forecasts of volatile time series. The multivariate Theil decomposition for the MSE and APOC criterion is used to compare and evaluate 3-dimensional VAR-GARCH-M time series forecasts for stock indices and exchange rates.

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File URL: http://www.rcfea.org/RePEc/pdf/wp23_13.pdf
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Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 23_13.

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Date of creation: May 2013
Handle: RePEc:rim:rimwps:23_13
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  1. Christoffersen, Peter F & Diebold, Francis X, 1996. "Further Results on Forecasting and Model Selection under Asymmetric Loss," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 561-571, Sept.-Oct.
  2. Lei Ren & Wolfgang Polasek, 2000. "A Multivariate Garch Model For Exchange Rates In The Us, Germany And Japan," Computing in Economics and Finance 2000 223, Society for Computational Economics.
  3. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
  4. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809.
  5. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
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