Makridakis, Spyros and Winkler, Robert L. 1983, "Averages of forecasts: Some empirical results," Management Science, Vol. 29, No. 9, pp. 987-996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....forecasts derived by similar methods also help. Surprisingly, the gains for combining across extrapolation methods were found to be greater than the results (Table 2) Armstrong [19841 found an average error reduction of 42 percent when two methods were combined (averaged over four studies) while Makridakis and Winkler [1983], in their study of 111 time series, found a 7.2 percent reduction for two methods, with continuing gains as methods were added (for example, a 16.3 percent reduction with five methods) Similar gains have been found when only econometric forecasts were averaged. For example, Brandon, Fritz and ....

Makridakis, Spyros and Winkler, Robert L. 1983, "Averages of forecasts: Some empirical results," Management Science, Vol. 29, No. 9, pp. 987-996.

....we propose combining the trained NNs using MSE OLCs. Combining the trained NNs may help integrate the knowledge acquired by the component NNs, and thus improves the resultant model accuracy. 1.1. 2 Why to combine neural networks In the literature on combining forecasts, Makridakis and Winkler [69] conclude: Thus, combining forecasts seems to be a reasonable practical alternative when, as often the case, a true model of the data generating process or a single best forecasting method cannot be or is not, for whatever reason, identified. This statement is equally applicable to ....

S. Makridakis and R. L. Winkler. Averages of forecasts: Some empirical results. Management Science, 29(9):987--996, 1983.

....of the single estimators under consideration is a simple but very efficient combined estimator. It proves successful in many practical studies and very often outperforms much more sophisticated combination techniques. A very comprehensive study of this kind is reported by Makridakis et al. 1982) Makridakis and Winkler (1983), and Winkler and Makridakis (1983) The arithmetic mean is more robust with respect to changes of the relative quality of the estimators than most other combination techniques. This appears to be the reason for its success and this is why the performance of the arithmetic mean is the touchstone ....

....a simple but very efficient combined estimator. It proves successful in many practical studies and very often outperforms much more sophisticated combination techniques. A very comprehensive study of this kind is reported by Makridakis et al. 1982) Makridakis and Winkler (1983) and Winkler and Makridakis (1983). The arithmetic mean is more robust with respect to changes of the relative quality of the estimators than most other combination techniques. This appears to be the reason for its success and this is why the performance of the arithmetic mean is the touchstone against which all other combination ....

Makridakis, S. and Winkler, R.L. (1983): Averages of forecasts: Some empirical results, Management Science 29, 987-996.

.... following: In the literature on combination of univariate forecasts it is a frequently stated observation, that estimating the optimal combination weights neglecting covariances between the estimators often leads to better combined estimates than calculation employing these covariances (see e.g. Makridakis and Winkler (1983)) Therefore, it may well be the case that employing covariances between the di erent components of the estimators is not bene cial as well. These covariances are employed by SCAT but not by MCAT or WCAT. 4 At rst glance it may seem counterintuitive that other estimators could produce better ....

.... 12 ) tr( b 11 b 22 2 b 12 ) 1 : As already mentioned in Section 2 in practice we can observe that estimating the optimal combination weights neglecting covariances between the estimators often leads to better combined estimates than calculation employing these covariances (cf. Makridakis and Winkler (1983)) Therefore, we will also investigate variants of the three covariance adjustment techniques neglecting covariances between estimators, i.e. assuming them to be 0, in the calculation of the combination weights. These variants will be referred to as g SCAT, g MCAT and g WCAT, respectively. g ....

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Makridakis, S. and Winkler, R.L. (1983): Averages of forecasts: Some empirical results, Management Science 29, 987-996.

....that homogeneous voting can only reduce variance and not bias. Some papers have also reported improved performance through non homogeneous voting, that is, voting multiple hypotheses that have been constructed by different learning algorithms applied to the same problem (Bates Granger, 1969; Makridakis Winkler, 1983; Clemen, 1989; Schapire, 1990; Hampshire II Waibel, 1990; Zhang, Mesirov, Waltz, 1992; Cardie, 1993; Quinlan, 1993b) Nonhomogeneous voting can reduce both bias and variance if the bias errors of the various algorithms are different. Error correcting output coding involves neither homogeneous ....

Makridakis, S., & Winkler, R. L. (1983). Averages of forecasts: Some empirical results. Management Sci., 29 (9), 987--996.

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