دانلود رایگان مقاله پازل ترکیب پیش بینی توضیح نظری ساده

abstract

This paper offers a theoretical explanation for the stylized fact that forecast combinations with estimated optimal weights often perform poorly in applications. The properties of the forecast combination are typically derived under the assumption that the weights are fixed, while in practice they need to be estimated. If the fact that the weights are random rather than fixed is taken into account during the optimality derivation, then the forecast combination will be biased (even when the original forecasts are unbiased), and its variance will be larger than in the fixed-weight case. In particular, there is no guarantee that the ‘optimal’ forecast combination will be better than the equal-weight case, or even improve on the original forecasts. We provide the underlying theory, some special cases, and a numerical illustration. Crown Copyright © 2016 Published by Elsevier B.V. on behalf of International Institute of Forecasters. All rights reserved.

5. Discussion

In their ‘simple explanation of the forecast puzzle’, Smith and Wallis (2009) offer three main conclusions in terms of the mean squared error of the forecast (MSFE). We now analyze these conclusions in the context of the theory developed in Section 3. Their first conclusion is that ‘[. . . ] a simple average of competing forecasts is expected to be more accurate, in terms of MSFE, than a combination based on estimated weights.’ This is the situation illustrated for two dimensions in Figs. 1 and 2. The combination with equal weights is unbiased, and its variance has only one component: ı ′Σyyı/m2 . In many situations, this leads to a smaller mean squared error than a biased combination with additional components d and δ, as given in Proposition 3.1, for the case where the weights are estimated.