優勢策略均衡於Nash非線性灰色柏努利模型的應用－以金磚四國股價指數預測為例

Application of Dominant Strategy Equilibrium to Nash Nonlinear Grey Bernoulli Model-An example of BRIC's Stock Indices Forecasting

10.6338/JDA.201506_10(3).0005

辛沛翰(Pei-Han Hsin)

灰預測 ； Nash均衡 ； 優勢策略 ； 股價指數 ； Grey forecasting ； Nash equilibrium ； Dominated Strategy ； Stock index

Journal of Data Analysis

10卷3期（2015 / 06 / 01）

95 - 114

繁體中文

傳統灰預測模型GM（1,1）在計算處理上是簡單的，但是缺乏高度模型預測能力。Chen (2008)與Chen et. al.（2008）提出Nonlinear grey Bernoulli model（NGBM），將模型冪次方變成可調整參數，大幅提升預測效果；Chen et. al.（2010）引入經濟學理論中的Nash均衡的求解概念，進而提出 Nash NGBM（NNGBM），其研究主要將微分方程式的次方（n）與係數（p）同時轉變成可調整參數，使得模型有更佳的預測能力。然而，Nash均衡解的多重性，也將發生在Nash NGBM之中。有鑑於此，本研究將搜尋最適解的起始點改變，進而找出其他Nash解，再利用優勢策略均衡概念，找出優勢策略Nash解。再者，本研究以已發表文章的個案驗證優勢策略Nash解具有之高度預測能力。最後，本文將上述灰色預測模型預測金磚四國的股票指數，結果發現建模效度依序是優勢策略NNGBM、NNGBM、NGBM以及GM；在金磚四國股價指數預測上皆預測未來五季呈現上揚牛市。

The traditional grey forecasting model is computationally simple but less highly accurate in forecasting. Chen (2008) and Chen et al., (2008) present the nonlinear grey Bernoulli model (NGBM) with adjustable power n to improve the GM (1,1). Chen, Hsin and Wu (2010) propose Nash NGBM with adjustable power n and coefficient p to enhance the forecast ability. However, the multiple solutions come out in Nash NGBM. Thus, this study tries to seek the other Nash solutions by changing the initial point of p. Then, find strictly/weakly dominant strategy among Nash solutions. Moreover, reexamine an example of a published paper to confirm the forecasting ability of the proposed method. Finally, apply the proposed method to predict BRIC's stock indices. The results show that NNGBM with dominant strategy equilibrium is best and BRIC's stock indices will be going up in the future.

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