本研究主要探討九個不同國家的股價指數：KOSPI（韓國KOSPI 股價指數）、NKI225（日經225 股價指數）、TAIEX（台灣加權股價指數）、DJIA（美國道瓊工業股價指數）、NDX（美國那史達克股價指數）、SPX（美國S&P500 股價指數）、CAC（法國CAC 40 股價指數）、FTSE（英國FTSE 100 股價指數）及 DAX（德國DAX 30 股價指數）波動度的特性，除了運用變幅單一變數來預測外，還將其拆成最高價及最低價二個變數，且分別利用 ARMA 模型、GARCH 模型、CARR 模型與 VECM 模型等不同波動度模型中配適出較適合各國股價指數波動度的模型。再者，本研究採用 Parkinson (1980）之變幅波動（range volatility）及報酬平方（squared return）作為真實波動度代理變數，並利用MSE、MAE、LLE、GMLE 等四種統計損失函數（loss function）及 VaR 財務績效評估，分別作為預測能力衡量指標，最後以 SPA 檢定各模型預測能力之優劣。實證結果為：當決策者使用 MAE 與 LLE 為損失函數時，則用 CARR 模型有較佳的預測能力；當決策者使用 MSE 與 GMLE 為損失函數時，則用 不對稱 GARCH 模型有較佳的預測能力。當決策者使用 VaR 財務績效評估時，除了 KOSPI、NKI225 和 TAIEX 是以不對稱 GARCH 模型有較佳的預測能力外，其餘股價指數皆是以 CARR 模型有較佳的預測能力。整體而言，由統計之觀點與財務之觀點來看波動度預測能力會得到相同的結論，各國股價指數不是以 CARR 模型預測較佳，就是以不對稱 GARCH 模型預測較佳。

This article selects the appropriate model to match volatility of nine stock markets from ARMA, GARCH, CARR and VECM models and use range, high and low variables to match the models. In the meantime, we use Parkinson (1980) proposed ranged-based estimator and squared return to be the proxy of true volatility. This study not only uses statistic loss functions, including MAE, MSE, LLE, GMLE and the VaR performance assessments are based on the range of measures that address the accuracy and efficiency, but also employ more robust SPA test to compare forecasting performance of models. The empirical result indicates that, for MAE and LLE, CARR model is preferred.In addition, for MSE and GMLE, asymmetric GARCH models are preferred.For VaR based loss function, except for KOSPI, NKI225 and TAIEX, CARR model is preferred.In a word, for statistic and financial loss functions, there are high performance to forecast volatility of nine stock markets which is CARR model or asymmetric GARCH model be used. Therefore, alternative stock markets and loss functions are important for volatility forecasting.

目       錄
第一章　緒　論	1
第一節　研究背景與動機	1
第二節　研究目的	4
第三節  研究架構	6
第二章　文獻回顧	8
第一節	波動特性之文獻	8
第二節	使用GARCH類模型預測波動之文獻	13
第三節  使用變幅預測波動之文獻	23
第三章　研究方法	28
第一節	單根檢定	28
第二節　ARCH效果檢定	31
第三節　條件變異數不對稱檢定	34
第四節　模型誤差分配之介紹	35
第五節　波動率的估計方式	37
第六節	樣本外預測	46
第七節	評估預測績效之方法	46
第八節	優勢預測能力檢定（Superior Predictive Ability Test）	54
第四章　實證結果分析	57
第一節　研究對象與資料處理	57
第二節	基本統計量分析	59
第三節　單根檢定	64
第四節　ARCH效果檢定	69
第五節　條件變異數不對稱檢定	70
第六節　Johansen共整合檢定	71
第七節　模型配適與估計	73
第八節　統計損失函數預測績效之比較	79
第九節　VaR 財務預測績效之比較	95
第五章　結論	105
參　考　文　獻	108
一、國外文獻	108
二、國內文獻	116

表　　　目　　　錄
【表4 - 2 - 1】各股價指數日報酬率之基本敘述統計量	60
【表4 - 2 - 2】各股價指數之DH基本敘述統計量	61
【表4 - 2 - 3】各股價指數之DL基本敘述統計量	62
【表4 - 2 - 4】各股價指數之Range基本敘述統計量	63
【表4 - 3 - 1】各股價指數報酬率之單根檢定	65
【表4 - 3 - 2】各股價指數DH之單根檢定	66
【表4 - 3 - 3】各股價指數DL之單根檢定	67
【表4 - 3 - 4】各股價指數Range之單根檢定	68
【表4 - 4 - 1】各股價指數報酬率之ARCH效果檢定	69
【表4 - 5 - 1】各股價指數報酬率之條件變異數不對稱檢定	70
【表4 - 6 - 1】Johansen共整合檢定	72
【表4 - 7 - 1】ARMA(A1與A2)模型下各股價指數之估計結果	75
【表4 - 7 - 1】ARMA(A1與A2)模型下各股價指數之估計結果(續)	76
【表4 - 7 - 2】VECM模型下各股價指數之估計結果	77
【表4 - 7 - 3】CARR與GARCH模型下各股價指數之估計結果	78
【表4 - 8 - 1】統計損失函數之 SPA 檢定(以Parkinson變幅為波動代理變數)	88
【表4 - 8 - 1】統計損失函數之 SPA 檢定(以Parkinson變幅為波動代理變數)(續)	89
【表4 - 8 - 2】統計損失函數之 SPA 檢定(以報酬率平方為波動代理變數)	91
【表4 - 8 - 2】統計損失函數之 SPA 檢定(以報酬率平方為波動代理變數)(續)	92
【表4 - 9 - 1】在各模型及各信心水準下各股價指數之平均 VaR 值	101
【表4 - 9 - 2】在各模型及各信心水準下各股價指數之非條件涵蓋率檢定	102
【表4 - 9 - 3】在各模型及各信心水準下各股價指數之條件涵蓋率檢定	103
【表4 - 9 - 4】各股價指數損失函數 MRC 之 SPA Test	104

圖　　　目　　　錄
【圖 1】研究流程圖	7

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