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Forecast Evaluations for Multiple Time Series: A Generalized Theil Decomposition

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  • Wolfgang Polasek

    (Institute of Advanced Studies, Austria)

Abstract

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.

Suggested Citation

  • Wolfgang Polasek, 2013. "Forecast Evaluations for Multiple Time Series: A Generalized Theil Decomposition," Working Paper series 23_13, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:23_13
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Wolfgang Polasek & Lei Ren, 2001. "Volatility analysis during the Asia crisis: a multivariate GARCH‐M model for stock returns in the U.S., Germany and Japan," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(1), pages 93-108, January.
    5. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521632423, September.
    6. 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.
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    Cited by:

    1. Bentour, El Mostafa, 2015. "A ranking of VAR and structural models in forecasting," MPRA Paper 61502, University Library of Munich, Germany.
    2. Aleksander Grechuta, 2018. "Porównanie trafności jednorocznych prognoz polskiej koniunktury sporządzanych przez krajowe i międzynarodowe instytucje ekonomiczne," Bank i Kredyt, Narodowy Bank Polski, vol. 49(1), pages 63-92.

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