總體經濟因素與股價關聯性之分析及預測－主成份迴歸、模糊線性迴歸及 Stein估計式

Abstract

本研究的目的在於探討總體經濟因素和股價間的關係，並試圖尋找股 價走勢之最佳預測模型。和相關文獻主要不同之處在於本研究以預測的角 度來進行模型的評比和選擇，這將直接反應單純以傳統方法決定之主成份 模型在預測上的表現。另外，本研究同時也引用統計決策理論中著名的 Stien估計式以及目前極為盛行的模糊線性迴歸來進行整合和改良，藉以 尋找優於傳統主成份迴歸之可能模型，以利投資者對股價走勢的瞭解，並 成為股價預測上的重要依據。除此之外，本研究的結果也提供其他需要進 行構面縮減和預測評比之研究的參考。研究結果顯示，整體而言以 Stein 估計式預測結果最具穩健性，非常值得採用。而以傳統方法決定之主成份 模型，在所有的主成份模型中幾乎敬陪末座。另外，模糊線性迴歸模型在 本研究的預測評估下，並沒有很好的表現。 The purpose of this paper is to find the best prediction model of Taiwan'sstock prices from twelve highly correlated macro-economic variables. Principalcomponents regression is one of the common methods of overcoming seriousmulticollinearity problem by modifying the method of ordinary least squares.But unfortunately principal components estimator may do much worse than ordinaryleast squares estimator if its components are not sufficiently close to the truedimensional space. Therefore Stein shrinkage estimator is constructed bycontracting the ordinary least squares estimator to the principal componentsestimator. However, in such a practical application of linear regression model,the linearity assumption for the particular relationship may be imprecise.Fuzzy methods have been proposed to represent a phenomenon that is imprecise andvague in nature. Under the criteria of prediction mean squared error, prediction mean absolute error and multivariate tests, we compare the ordinaryleast squares regression, principal components regression, Stein estimation withtheir fuzzy counterparts. In addition, the principal components models with theprincipal components retained by the Kaiser's rule, scree test and cumulatedproportion of variance rule are also discussed.