本研究以美國個股（微軟、亞馬遜）、股價指數（S&P 500指數、那斯達克綜合指數）與指數型股票基金（道瓊工業平均指數基金）自2001年1月至2010年5月之日資料為實證標的，探討加入日變幅（PK）、已實現波動率（RV）、已實現變幅（RRV）與已實現雙冪次變異（RBP）等波動估計式對於GARCH模型樣本外預測能力的提升效果。分別以PK及RV作為市場真實波動的代理變數，並採用各種損失函數評估各波動模型的預測績效。
本文以五分鐘頻率之日內資料來估計RV、RRV與RBP，進一步探討高頻率資料的效果。實證發現，各種波動估計式對GARCH模型波動預測存在不同程度的提升效果，其中又以RV、RRV及RBP等高頻日內資料為基礎之波動估計式表現較佳。而以RV及PK作為真實波動性之代理變數下的預測績效比較結果趨於一致，證明預測結果的穩健性，也另外說明除了RV適合作為真實波動性之代理變數外，PK也是個不錯選擇。
另外，波動估計式對於提升波動模型預測績效的程度會因標的不同而
有所差異，本文研究發現在個股方面的提升效果最佳，此結果隱含在波動性較大的標的下更能顯現波動估計式的效果，因此投資者在投資高波動性之金融商品時，可應用波動估計式提升模型的波動性預測績效。

This paper augments the GARCH models with the PK range, realized volatility (RV), realized range volatility (RRV) and realized bipower variation (RBP). We investigate the impact of these volatility estimators by examining their out-of-sample forecast-improved. The data for our empirical study consists of individual stocks (Amazon and Microsoft), stock indices (S&P 500 and Nasdaq) and exchange traded fund (Dow Jones Industrial Average ETF) price quotes covering the period from 16 January 2001 to 28 May 2010. The forecast performance evaluation is relied on several loss functions and utilizing PK and RV as a proxy for true volatility. RV, RRV and RBP are intraday-based 
Volatilities which are obtained from intraday prices at 5-min frequency. So we can study the effect of high frequency data. Empirical results indicate that all volatility estimators can improve predictive ability. Especially, the inclusion of
intraday-based volatility measure in GARCH models notably improves forecasts. In most cases, the forecasting performances of models are almost consistent which are robust to alternative proxy measures, indicating that the PK is a useful alternative to the RV since daily high-low price data are readily available for most financial assets.
	Additionally, the degree of incremental predictive content of these volatility estimators varies from the data used. The volatility estimator provides the most incremental predictive content on individual stock. It implies that the volatility estimator can be more advantageous with higher volatility commodity. Thus, market practitioners can exploit the information content implied by these volatility estimators to improve forecast accuracy of models when they invest in financial instruments with higher volatility.

第一章	緒論	1
第一節	研究背景與動機	1
第二節	研究目的	3
第三節	研究架構	5
第四節	研究流程圖	6
第二章	文獻回顧	7
第一節	波動性預測模型	7
第二節	GARCH族預測能力比較之相關文獻	11
第三節	加入外生變數的增廣GARCH模型及日內資料相關文獻	17
第三章	研究方法	27
第一節	單根檢定	27
第二節	ARCH效果檢定	29
第三節	SGT分配	31
第四節	波動估計式	33
第五節	波動性預測模型架構	36
第六節	模型預測能力比較	38
第四章	實證結果	40
第一節	資料之基本分析	40
一、	資料來源與處理	40
二、	基本統計量分析	41
第二節	單根檢定與ARCH效果檢定之結果	46
一、	單根檢定	46
二、	ARCH效果檢定	49
第三節	波動模型之參數估計結果	50
第四節	模型預測能力比較	54
五、	結論	66
參考文獻	68
一、	國內文獻	68
二、	國外文獻	70

表目錄
【表2.3.1】加入隱含波動率對波動性預測能力的提升效果	18
【表2.3.2】加入成交量對波動性預測能力的提升效果	20
【表2.3.3】不同樣本外預測期間下績效改善之比較	22
【表2.3.4】加入RV之模型預測能力提升效果比較	22
【表2.3.5】加入PK之模型預測能力提升效果比較	23
【表2.3.6】加入各解釋變數之文獻整理	25
【表4.1.1】基本統計量之分析	42
【表4.1.1】基本統計量之分析（續）	43
【表4.2.1】時間序列資料之ADF單根檢定	47
【表4.2.2】時間序列資料之PP單根檢定	48
【表4.2.3】ARCH效果之檢定結果	49
【表4.3.1】個股波動模型參數估計結果	51
【表4.3.2】股價指數波動模型參數估計結果	52
【表4.3.3】指數型基金波動模型參數估計結果	53
【表4.4.1】波動性預測能力比較-以RV為代理變數	58
【表4.4.1】波動性預測能力比較-以RV為代理變數（續）	59
【表4.4.1】波動性預測能力比較-以RV為代理變數（續）	60
【表4.4.2】波動性預測能力比較-以PK為代理變數	61
【表4.4.2】波動性預測能力比較-以PK為代理變數（續）	62
【表4.4.2】波動性預測能力比較-以PK為代理變數（續）	63
【表4.3.3】加入波動估計式績效提升之比較	65
【表4.3.4】加入RV之績效提升比較	65

圖目錄
【圖1.4】研究流程圖	6
【圖3.3.1】SGT分配和標準常態分配比較圖	32
【圖4.1.1】亞馬遜之時間序列資料趨勢圖	44
【圖4.1.2】微軟之時間序列資料趨勢圖	44
【圖4.1.3】S&P 500股價指數之時間序列資料趨勢圖	44
【圖4.1.4】那斯達克股價指數之時間序列資料趨勢圖	45
【圖4.1.5】道瓊工業指數型基金之時間序列資料趨勢圖	45
【圖4.4.1】真實波動性之代理變數走勢圖-亞馬遜	55
【圖4.4.2】真實波動性之代理變數走勢圖-微軟	55
【圖4.4.3】真實波動性之代理變數走勢圖-S&P500股價指數	55
【圖4.4.4】真實波動性之代理變數走勢圖-那斯達克股價指數	56
【圖4.4.5】真實波動性之代理變數走勢圖-道瓊工業指數型基金	56

國內文獻
1.	王祝三、莊益源、張鐘霖（2003)，「波動率模型預測能力的比較--以臺指選擇權為例」，台灣金融財務季刊第四輯第二期，頁41-63。
2.	林思吟、洪瑞成、顏偉倫（2007)，「GARCH 模型的波動預測績效比較」，2007年健康與管理學術研討會
3.	林育秀（2008），「新台幣對人民幣與美元的匯率波動對台灣出口的影響」，朝陽科技大學財務金融系碩士學位論文。
4.	林秀蓉（2008)，「股價波動性預測」，淡江大學財務金融學系碩士學位論文。
5.	李沃牆、張克群（2006)，「比較不同波動率模型下台灣股票選擇權之評價績效」，真理財經學報，第14期，頁71-96。
6.	周秋如（2010)，「原油期貨報酬條件波動度預測績效：對稱與不對稱條件波動模型之比較」，嶺東科技大學財務金融研究所碩士論文。
7.	周雨田、巫春洲、劉炳麟（2004)，「動態波動模型預測能力之比較與實證」，財金論文叢刊，第一期，頁1-23。
8.	賈景宇（2001)，「台灣創新型認購權證在不同波動性模型下之比較」，中原大學企業管理學系碩士學位論文。
9.	陳佳琪（2008)，「原油價格波動性預測」，淡江大學財務金融學系碩士學位論文。
10.	陳煒朋（1999)，「GARCH模型與隱含波動性模型預測能之比較」，淡江大學財務金融研究所碩士論文。
11.	曾彥錤（2004)，「GARCH系列模型與台指選擇權VIX指數波動性預測能力之比較」，淡江大學財務金融學系碩士學位論文。
12.	鄒紹輝（2006)，「隱含波動率之模型及預測：以台灣市場為例」，國立中央大學統計研究所碩士學位論文。
13.	廖偉真（2009），「不同樣本頻率之股市波動性估計」，國立台灣大學生物資源暨農學院農業經濟研究所碩士學位論文。
14.	蔡麗茹、葉銀華（2000)，「不對稱GARCH族模型預測能力之比較研究」，輔仁管理評論，第七卷，第一期，頁183-196。
15.	鄭婉秀、鄒易凭、蘇欣玫（2006)，「商品期貨波動性之預測：CARR模型之應用」，朝陽商管評論，第五卷，第二期，頁115-132。

國外文獻
1.	Akgiray, V. (1989). Conditional heteroscedasticity in time series of stock returns:
evidence and forecasts, Journal of Business, 62, 55-80.
2.	Andersen, T. G, and Bollerslev, T. (1997). Heterogeneous information arrivals and return volatility dynamics: Uncovering the long run in high frequency returns, Journal of Finance, 52, 975-1005.
3.	Andersen, T. G, and Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts, International Economic Review, 39(4), 885-905.
4.	Brooks, C. (1998). Predicting stock index volatility: Can market volume help? Journal of Forecasting, 17, 59-80.
5.	Barndorff-Nielsen, O. E., and Shephard, N. (2002a). Econometric analysis of realised volatility and its use in estimating stochastic volatility models, Journal of the Royal Statistical Society, Series B, 64, 253–280.
6.	Barndorff-Nielsen, O. E., and Shephard, N. (2002b).Estimating quadratic variation using realised variance, Journal of Applied Econometrics, 17, 457–477.
7.	Barndorff-Nielsen, O. E., and Shephard, N. (2004a). Econometrics of testing for jumps in financial economics using bipower variation, Journal of Financial Econometrics, 4, 1–30.
8.	Barndorff-Nielsen, O. E., and Shephard, N. (2004b). Power and bipower variation with stochastic volatility and jumps, Journal of Financial Econometrics, 2, 1–48.
9.	Becker, R., Clements, A. E., and White, S. I. (2007). Does implied volatility provide any information beyond that captured in model-based volatility forecasts
10.	Black, F. (1976). Studies of stock price volatility changes, Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economics
Statistics Section, 177-181.
11.	Blair, B.J., Poon, S.H., and Taylor, S.T. (2001). Forecasting S&P100 volatility: the incremental information con tent of implied volatilities and high-frequency index returns, Journal of Econometrics, 105, 5-26.
12.	Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity,
Journal of Econometrics, 31, 307-327.
13.	Box, G. E. P., and Jenkins, G. M. (1976). Time series analysis : Forecasting and control, 2nd edition, San Francisco: Holden-Day.
14.	Busch, T., Christensen, B. J., and Nielsen, M. O (2010).The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets, Journal of Econometrics, 160, 48-57.
15.	Campbell, J. Y. and Hentschel, L. (1992). No news is good news: An asymmetric
model of changing volatility in stock returns, Journal of Financial Economics, 31, 281-318.
16.	Chou, R. Y. (2005). Forecasting financial volatilities with extreme values: the conditional autoregressive range (CARR) Model. Journal of Money, Credit, and Banking, 37: 561-582. 
17.	Christie, A. A. (1982). The stochastic behavior of common stock variances, Journal of Financial Economic, 10, 407-432.
18.	Christensen, K., and Podolskij, M. (2007). Realised range-based estimation of integrated variance, Journal of Econometrics, 141, 323–349.
19.	Corrado, C ., and Truong, C. (2007). Forecasting stock index volatility: Comparing implied volatility and the intraday high-low price range, Journal of Financial Research, 201-215.
20.	Donaldson, G., and Kamstra, M. (2004).Volatility forecasts, trading volume, and the ARCH versus option-implied volatility trade-off, Working Paper 6.
21.	Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of variance of UK inflation, Econometrica, 50, 987-1008..
22.	Engle, R. F., and Bollerslev, T. (1986). Modelling the persistence of conditional variances, Econometric Reviews, 5, 1-50.
23.	Engle, R. F., Lilien, D. M., and Robins R. P. (1987). Estimating time varying risk premia in the term structure: the ARCH-M model, Econometric, 55, 391-407
24.	Engle, R. F., and Ng, V. K. (1993). Measuring and testing the impact of news on volatility, Journal of Finance, 48, 1749-1778.
25.	Evans, T., and Mcmillan, D.G. (2007). Volatility forecasts: the role of asymmetric and long-memory dynamics and regional evidence, Applied Financial Economics, 17, 1421-1430.
26.	Fama, E. F. (1965). The behavior of stock market prices, Journal of Business, 38,
34-105.
27.	Fuertes, A. M., Izzeldin, M., and Kalotychou E. (2009).On forecasting daily stock volatility: The role of intraday information and market conditions, International Journal of Forecasting, 25, 259-281.
28.	Garman, M.B., and Klass, M.J. (1980). On the estimation of security price volatilities from historical data, Journal of Business, 53, 67–78.
29.	Girard, E., Biswas, R. (2007). Trading volume and market volatility: Developed versus emerging stock markets, Financial Review, 42, 429-529.
30.	Glosten, L.R., Jagannathan, R., and Runkle, D.E. (1993）. On the relation between the expected value and volatility on the nominal excess returns of stocks, Journal of Finance, 48, 1779-1801.
31.	Granger, C. W. J., and Newbold, P. (1974）. Spurious regressions in econometrics, Journal of Econometrics, 2, 111-120.
32.	Koopman, S.J., Jungbacker, B., and Hol, E. (2005). Forecasting daily variability of the S&P100 stock index using historical, realized and implied volatility measurements, Journal of Empirical Finance, 12, 445-475.
33.	Le, V., and Zurbruegg, R. (2010）.The role of trading volume in volatility forecasting, Journal of international Financial Markets, Institutions and Money.
34.	Luu, J. C., and Martens, M. (2002）. Testing the mixture of distributions hypothesis using realized volatility. Journal of Futures Markets, 23, 661-679.
35.	Mandelbrot, B. (1963). The variation of certain speculative prices, Journal of
Business, 36, 394-419.
36.	Martens, M. (2001）.Forecasting daily exchange return volatility using intraday returns. Journal of International Money and Finance, 20, 1-23.
37.	Martens, M. (2002) Measuring and forecasting S&P 500 index-futures volatility using high-frequency data, Journal of Futures Markets, 22, 497-518.
38.	McMillan, D. G., and Speight, A. E. H. (2004). Daily volatility forecasts: Reassessing the performance of GARCH models, Journal of Forecasting, 23, 449-460.
39.	Morgan, I. G. (1976). Stock prices and heteroscedasticity, Journal of Business, 49, 496-508.
40.	Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach, Econometrica, 59, 347-370.
41.	Parkinson, M. (1980). The extreme value method for estimating the variance of the rate of return, Journal of Business, 53, 61-65.
42.	Ripple, R. D., and Moosa, I. A. (2009). The effect of maturity, trading volume, and open interest on crude oil futures price range-based volatility, Global Finance Journal, 20, 209-219.
43.	Rogers, L.C.G., and Satchell, S.E. (1991). Estimating variance from high, low and closing prices, Annals of Applied Probability, 1, 504–512.
44.	Schwert, G.W., and Seguin, P. J. (1990). Heteroskedasticity in stock returns, Journal of Finance, 45, 1129-1155.
45.	Theodossiou, P. (1998), Financial data and the skewed generalized t distribution,
Management Science 44, 1650-1661.
46.	Zakoian, J.M. (1994）. Threshold heteroskedastic models, Journal of Economic Dynamics and Control, 18, 931-955.