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RECURSIVE FORECAST COMBINATION FOR DEPENDENT HETEROGENEOUS DATA

Published online by Cambridge University Press:  30 September 2009

Abstract

This paper studies a procedure to combine individual forecasts that achieve theoretical optimal performance. The results apply to a wide variety of loss functions and only require a tail condition on the data sequences. The theoretical results show that the bounds are also valid in the case of time varying combination weights.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

I am grateful to two anonymous referees and a co-editor for comments that improved the paper in both content and presentation.

References

REFERENCES

Aiolfi, M. & Timmermann, A. (2006) Persistence in forecasting performance and conditional combination strategies. Journal of Econometrics 135, 3153.Google Scholar
Andrews, D. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821856.Google Scholar
Bai, J. & Perron, P. (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66, 4778.10.2307/2998540CrossRefGoogle Scholar
Breiman, L. (1961) Optimal gambling systems for favorable games. In Neyman, J. (ed.), Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability 1, 6578. University of California Press.Google Scholar
Breiman, L. (1996) Heuristics of instability and stabilization in model selection. Annals of Statistics 24, 23502383.Google Scholar
Cesa-Bianchi, N. (1999) Analysis of two gradient-based algorithms for online regression. Journal of Computer and System Sciences 59, 392411.CrossRefGoogle Scholar
Cesa-Bianchi, N. & Lugosi, G. (2006) Prediction, Learning, and Games. Cambridge University Press.10.1017/CBO9780511546921CrossRefGoogle Scholar
Chen, Z. & Yang, Y. (2007) Time series models for forecasting: Testing or combining? Studies in Nonlinear Dynamics & Econometrics 11, no. 1, article 3. Downloadable: http://www.bepress.com/snde/vol11/iss1/art3.Google Scholar
Cover, T. (1991) Universal portfolios. Mathematical Finance 1, 129.10.1111/j.1467-9965.1991.tb00002.xGoogle Scholar
Cross, J.E. & Barron, A.R. (2003) Efficient universal portfolios for past dependent target classes. Mathematical Finance 13, 245276.CrossRefGoogle Scholar
Dawid, A.P. (1984) Present position and potential developments: Some personal views: Statistical theory: The prequential approach. Journal of the Royal Statistical Society, Series A 147, 278292.10.2307/2981683CrossRefGoogle Scholar
Dawid, A.P. (1997) Prequential analysis. In Kotz, S., Read, C.B., & Banks, D.L. (eds.), Encyclopedia of Statistical Sciences, vol. 1, pp. 464470. Wiley.Google Scholar
Deutsch, M., Granger, C.W.J., & Teräsvirta, T. (1994) The combination of forecasts using changing weights. International Journal of Forecasting 10, 4757.10.1016/0169-2070(94)90049-3CrossRefGoogle Scholar
Devroye, L., Györfi, L., & Lugosi, G. (1996) A Probabilistic Theory of Pattern Recognition. Springer-Verlag.CrossRefGoogle Scholar
Diebold, F.X. & Pauly, P. (1990) The use of prior information in forecast combination. International Journal of Forecasting 6, 503508.CrossRefGoogle Scholar
Elliott, G. & Timmermann, A. (2004) Optimal forecast combinations under general loss functions and forecast error distributions. Journal of Econometrics 122, 4779.Google Scholar
Györfi, L., Lugosi, G., & Udina, F. (2006) Nonparametric kernel-based sequential investment strategies. Mathematical Finance 16, 337358.CrossRefGoogle Scholar
Helmbold, D.P., Schapire, R.E., Singer, Y., & Warmuth, M.K. (1998) Online portfolio selection using multiplicative updates. Mathematical Finance 8, 325347.10.1111/1467-9965.00058Google Scholar
Hendry, D.F. & Clements, M.P. (2004) Pooling of forecasts. Econometrics Journal 7, 131.CrossRefGoogle Scholar
Herbster, M. & Warmuth, M.K. (2001) Tracking the best linear predictor. Journal of Machine Learning Research 1, 281309.Google Scholar
Kivinen, J. & Warmuth, M.K. (1997) Exponentiated gradient versus gradient descent for linear predictors. Information and Computation 132, 163.10.1006/inco.1996.2612Google Scholar
Leung, G. & Barron, A.R. (2006) Information theory and mixing least-squares regressions. IEEE Transactions on Information Theory 52, 33963410.CrossRefGoogle Scholar
Nikandrova, A. (2005) Universal portfolios selection from a practical perspective. Masters Dissertation, Faculty of Economics, University of Cambridge.Google Scholar
Pesaran, M.H. & Timmermann, A. (2005) Real time econometrics. Econometric Theory 21, 212231.CrossRefGoogle Scholar
Samuelson, P.A. (1979) Why we should not make mean log of wealth big though years to act are long. Journal of Banking and Finance 3, 305307.Google Scholar
Sancetta, A. (2007) Online forecast combinations of distributions: Worst case bounds. Journal of Econometrics 141, 621651.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2004) Combination forecasts of output growth in a seven-country data set. Journal of Forecasting 23, 405430.Google Scholar
Timmermann, A. (2006) Forecast combinations. In Elliott, G., Granger, C.W.J., & Timmermann, A. (eds.), Handbook of Economic Forecasting 1, pp. 135196. Elsevier.Google Scholar
Vapnik, V. (1998) Statistical Learning Theory. Wiley.Google Scholar
Vovk, V. (1990) Aggregating strategies. In Fulk, M.A. (ed.), Proceedings of the 3rd Annual Workshop on Computational Learning Theory, pp. 371386. Morgan Kaufmann. Downloadable: http://www.vovk.net/aa/01.zip.Google Scholar
Yang, Y. (2004) Combining forecasting procedures: Some theoretical results. Econometric Theory 20, 176222.10.1017/S0266466604201086Google Scholar
Zou, H. & Yang, Y. (2004) Combining time series models for forecasting. International Journal of Forecasting 20, 6984.10.1016/S0169-2070(03)00004-9Google Scholar