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題名 | A Diagrammatic Exposition of the Combining Weights under the Error-variance Minimizing Criterion=最小誤差準則下預測組合權數之幾何闡釋 |
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作 者 | 梁國源; | 書刊名 | 東吳經濟商學學報 |
卷期 | 29 2000.06[民89.06] |
頁次 | 頁65-74 |
分類號 | 550.1 |
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; |
語文 | 英文(English) |
中文摘要 | 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。 |
英文摘要 | 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) |
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