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題名：A Diagrammatic Exposition of the Combining Weights under the Error-variance Minimizing Criterion
書刊名：東吳經濟商學學報
作者：梁國源
作者(外文)：Liang, Kuo-yuan
出版日期：2000
卷期：29
頁次：頁65-74
主題關鍵詞：預測組合；最小誤差變異準則；超平面；位向；二次式；Combination of forecasts；Error-variance minimizing criterion；Hyperplane；Orientation；Quadratic form
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本文透過二次式 (eqadraticform)、超平面 (hyperplane) 與位向 (orientation) 等線性代數用語之概念，闡釋最小誤差變異準則 (error-varianceminimizing criterion) 下最佳預測組合權數之幾何意義。
This note looks into some of the core ideas of the well-known combining formula of Bates-Granger-Newbold-Reid and also the corresponding sign-determination rule of the optimal combining weights under the error-variance minimizing criterion by means of a set of diagrams. These geometric constructions, instructive in itself, highlight intuition behind the algebraic formula. In particular, the optimal location in the weight space is demonstrated to occur at a point where a surface of an ellipsoid w'Σw = r2 is tangent to the hyperplane w'v = 1. The geometric illustrations can also depict the possibilities of the combination of two positive weights as wel1 as a positive and a negative weight. (JEL:C53)
期刊論文
1.Clemen, R. T.(1989)。Combining Forecasts: A Review and Annotated Bibliography。International Journal of Forecasting，5(4)，559-583。  new window
2.Newbold, P.、Granger, C. W. J.(1974)。Experience with Forecasting Univariate Time Series and Combination of Forecasts。Journal of Royal Statistical Society, Series A，137(2)，131-165。  new window
3.Fair, R. C.、Shiller, R. J.(1990)。Comparing Information in Forecasts from Econometric Models。American Economic Review，80(3)，375-389。  new window
4.Bates, J. M.、Granger, C. W. J.(1969)。The Combination of Forecasts。Operational Research Quarterly，20(4)，451-468。  new window
其他
1.Banchoff, T. and J. Wermer(1983)。Linear Algebra Through Geometry，New York：Springer-Verlag。  new window
2.Bunn, D. W.(1985)。Statistical Efficiency in the Linear Combination of Forecast。  new window
3.Die old, F. X.(1989)。Forecast Combination and Encompassing: Reconciling Two Divergent Literatures。  new window
4.Holden, K., D. A. Peel, and J. L. Thompson(1990)。Economic Forecasting: An Introduction，Cambridge：Cambridge University Press。  new window
5.Liang, K. Y.(1992)。On the Sign of Optimal Combining Weights under the Error-variance Minimizing Criterion。  new window
6.Liang, K. Y and Y. C. Shih(1994)。Bayesian Composite Forecasts: An Extension and a Clarification。  new window
7.Nelson, C. R.(1972)。The Prediction Performance of the FRB-MIT-PENN Model of the U. S. Economy。  new window
8.Poirier, D. J.(1995)。Intermediate Statistics and Econometrics，Cambridge：The MIT Press。  new window
9.Ramanathan, R.(1992)。Introductory Econometrics with Applications，Orlando, Florida：Harcourt Brace Jovanovich。  new window
10.Reid, D. J.(1969)。A Comparative Study of Time-Series Prediction Techniques on Economic Data。  new window
11.Wallis, K. F.(1989)。Macroeconomic Forecasting: A Survey。  new window
12.Winkler, R. L.(1981)。Combining Probability Distributions from Different Information Sources。  new window
13.Winkler, R. L.(1989)。Combining Forecasts: A Philosophical Basis and Some Current Issues。  new window
 
 
 
 
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