混沌理論在台灣證券市場的碎形結構分析與其應用在投資組合風險分散效果評估

Abstract

本論文嘗試以碎形理論來剖析臺灣股票市場報酬率﹐研究資料範圍為民國 六十年至民國八十五年所有上市股票收盤價資料﹐研究工具為R/S Analysi。R/S Analysis 以辨識出系統的長期記憶性與非週期性循環﹐估 計出Hurst係數、碎形維度、光譜係數與特徵係數。研究過程中﹐為降低 短期記憶性對R/S Analysi的干擾﹐本研究先將資料取一階AR( autoregressi殘差﹐並以趨勢修正模式去除短期波動的影響﹐以加強估計 的準確性。本研究將推估台灣股市加權指數與所有普通股日報酬率資料的 Hurs係數與穩定分配中的特徵係數﹐藉此了解傳統統計模式所不能表現的 碎形結構與市場風險。在碎形市場驗證方面﹐首先建立虛無假設為高斯分 配﹐若H顯著大於0.便拒絕虛無假設﹐亦即系統在信賴水準下符合碎形市 場假設。 The prime objective in this paper is to reveal the fractal structureof Taiwan Stock Market, and to apply the adaptation of fractal marketanalysis on the portfolio theory. In this study, R/S analysis is used as the primary analytical tool for uncovering long memory effects, fractal statistical structure, and the presence of cycles. Meanwhile, the following three subjects are examined: First, estimation of Hurst exponents and charac-teristic exponents, and testing of random null hypothesis in the samples of TSE-WPSI and 295 common stocks. Second, comparison and testing on three alternative R/S methods, and they are standard, with taking AR(1) residuals, and with trend correction. Third, evaluation and testing on the difference of diversification effects variousαportfolios. The results are shown that Taiwan Stock Market can be well characterized by the fractal structure. With respect to the preceding subjects : First, there is a persistent trend existing in WPSI and its non- periodic cycle length is equal to 4 years. Second, the R/S analysis with taking AR(1) residuals and trend correction yields a better estimation of Hurst exponent. Third, the difference on diversification effects between variousα portfolio is not significant by empirical results.