Forecast Evaluations for Multiple Time Series: A Generalized Theil Decomposition
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Christoffersen & Diebold, "undated". "Further Results on Forecasting and Model Selection Under Asymmetric Loss," Home Pages _059, University of Pennsylvania.
- 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.
- 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.
- Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-263, July.
- Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
- Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809, November.
- 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. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:rim:rimwps:23_13. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marco Savioli)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.