Model Averaging by Stacking


The paper introduces a new Frequentist model averaging estimation procedure, based on a stacked OLS estimator across models, implementable on cross-sectional, panel, as well as time series data. The proposed estimator shows the same optimal properties of the OLS estimator under the usual set of assumptions concerning the population regression model. Relatively to available alternative approaches, it has the advantage of performing model averaging exante in a single step, optimally selecting models’ weight according to the MSE metric, i.e. by minimizing the squared Euclidean distance between actual and predicted value vectors. Moreover, it is straightforward to implement, only requiring the estimation of a single OLS augmented regression. By exploiting exante a broader information set and benefiting of more degrees of freedom, the proposed approach yields more accurate and (relatively) more efficient estimation than available expost methods.

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Morana, C. (2015) Model Averaging by Stacking. Open Journal of Statistics, 5, 797-807. doi: 10.4236/ojs.2015.57079.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Baiardi, D. and Morana, C. Financial Deepening and Income Distribution Inequality in the Euro Area. Department of Economics, Management and Statistics, University of Milan Bicocca, Working Paper No. 316.
[2] Claeskens, G. and Hjort, N. (2008) Model Selection and Model Averaging. Cambridge University Press, Cambridge.
[3] Hendry, D.F. and Doornik, J.A. (2004) Empirical Model Discovery and Theory Evaluation. MIT Press, Cambridge.
[4] Hoeting, J.A., Madigan, D., Raftery, A.E. and Volinsky, C.T. (1999) Bayesian Model Averaging: A Tutorial. Statistical Science, 14, 382-417.
[5] Moral Benito, E. (2015) Model Averaging in Economics: An Overview. Journal of Economic Surveys, 29, 46-75.
[6] Buckland, S., Burnham, K. and Augustin, N. (1997) Model Selection: An Integral Part of Inference. Biometrics, 53, 603-618.
[7] Hansen, B. (2007) Least Squares Model Averaging. Econometrica, 75, 1175-1180.
[8] Hansen, B. and Rancine, J. (2010) Jacknife Model Averaging. Journal of Econometrics, 167, 38-46.
[9] Hayashi, F. (2000) Econometrics. Princeton University Press, Princeton.

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