能源的充足與否對於人類一直是一項重大的議題，而美國大片頁岩層中之石油蘊藏量雖大，但過去受限於開採技術不成熟被認為沒有開採價值，但自21世紀以降，隨著水平鑽深與高水壓裂岩的技術漸趨成熟，使得開採頁岩層中的石油成為了可行且符合成本的辦法。頁岩油之產地主要集中於美國，本研究利用EIA(美國能源資訊協會)所公布之每年之頁岩油日均產量，並分別使用單變數GARCH模型及Cholesky分解之Matrix-diagonal模型，輔以TGARCH模型中槓桿效應之觀念，以估計西德州原油、布蘭特原油及杜拜原油報酬率之模型。
本研究實證結果顯示，由頁岩油所設置之虛擬變數於單變數GARCH中為顯著，但其於三變數之MGARCH模型中則顯示係數不顯著，其原因可能為頁岩油之產量相較傳統石油之產量仍太低，其對於國際石油價格之影響不大因此被模型中其他項所造成之影響取代，且受限於其資料為年資料，僅能設置虛擬變數以代表之。本研究透過門檻項、自我相關項及交叉相關項之設定，除了使各個GARCH模型之係數統計結果均顯著以外，且皆能通過殘差自我相關檢定。

Energy’s sufficiency is always one of the most important issues to human. U.S. always has a great deposit of oil shale, but extracting tight oil from it was too expensive due to lack of technology in the past. After 21st century, as the technology of horizontal well and hydraulic fracturing becoming more and more matured, it became practicable and cost-effective to extract tight oil from oil shale. Most of the production of tight oil in the world is in U.S., so it will be proper to use the data of U.S. tight oil production (million barrels per day) to represent the world shale oil production, and we get the data from EIA (U.S. Energy Information Administration). We run those data separately by using univariate GARCH model and Cholesky decomposition’s Matrix-diagonal multivariate GARCH model to estimate the model of West Texas Intermediate, Dubai, and Brent crude oil price’s return rate.
The outcome models show that the dummy variable that we set for the tight oil production will be significant in the univariate GARCH model, but it is not the case in the multivariate GARCH model. Possible reasons may be the tight oil production is still too low compared to the conventional crude oil production, so its influence is too low and be replaced by the other variables; and the data of the tight oil is yearly so that we can only set a dummy variable to represent it. With the settings of threshold variables, self-correlated variables, and cross-correlated variables, the estimated GARCH model’s coefficients are all significant, and can all pass the autocorrelation test.

誌謝 i
中文摘要 ii
ABSTRACT iii
CONTENTS iv
LIST OF FIGURES vii
LIST OF TABLES viii
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 1
第三節 研究架構 2
第二章 文獻回顧 3
第一節 應用GARCH模型分析油價之文獻 3
<一> Claudio Morano (2001) 3
<二> Hassan Mohammadi (2010) 3
第二節 研究方法之文獻 3
<一> C. W. J. Granger and P. Newbold (1974) 3
<二> Engle, R. F. (1982) 3
<三> Bollerslev, T. (1986) 4
<四> Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993) 4
<五> Ding, Z. and Engle, R. F. (2001) 4
第三章 研究方法 5
第一節 單根檢定 5
第二節 殘差相關之檢定 6
<一> Q統計量 6
<二> Q2統計量 7
第三節 模型選擇準則-AIC與SBC 7
第四節 ARCH與GARCH模型 7
<一> ARCH模型 7
<二> GARCH模型 8
<三> TGARCH模型 8
第五節 矩陣對角化模型(Matrix-Diagonal Model) 9
第四章 實證結果分析 10
第一節 資料描述 10
<一> 研究樣本 10
<二> 資料趨勢圖 10
第二節 單根檢定 13
第三節 GARCH模型建立 14
<一> 單變數GARCH模型建構 14
<二> 雙變數GARCH模型建構 17
<三> 三變數GARCH模型建構 25
第五章 研究結論與建議 29
第一節 研究結論 29
第二節 研究建議與未來研究方向 30
參考文獻 32

中文文獻:
[1]楊奕農，2009，時間序列分析:經濟與財務上之應用(二版)，雙葉書廊出版。
[2]陳旭昇，2007，時間序列分析:總體經濟與財務金融支應用，東華書局出版。
[3]劉筱筠，2005，“應用門檻GARCH-M模型分析國際原油價格變動與台灣股價報酬波動之關聯”，國立台北大學經濟學系碩士論文。
[4]蔡坤旻，2009，“原油價格變動對於太陽能產業指數的影響-雙門檻GARCH模型之應用-”，國立台北大學國際企業研究所碩士論文。
[5]陳維邦，2008，“股價與石油價格波動性之關係- 動態條件相關多變量模型之應用-”，逢甲大學財務金融學系碩士論文。
[6]庄&;#32418;&;#38892;，2013，“頁岩革命的真相(一): “世界工廠”或將迴歸美國”， http://finance.people.com.cn/n/2013/1101/c348883-23397597.html
[7]庄&;#32418;&;#38892;，2013，“頁岩革命的真相(二): 中國尚難以複製美國的成功”， http://finance.people.com.cn/BIG5/n/2013/1104/c348883-23419898.html
[8]羅比特。斯吉德爾斯基，2013，“頁岩油真的是全球經濟的終極救星?”， http://www.businessweekly.com.tw/KBlogArticle.aspx?ID=5734&;pnumber=1
[9]方文碩、田志遠，2001，“匯率貶值對股票市場的衝擊-雙變量GARCH-M模型”，台灣金融財務季刊，第二輯第三期， pp.99-117。
英文文獻:
[1]Bollerslev, T., 1986, “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, 31, pp.307-327.
[2]Bollerslev, T., R. Chou, and F. Kroner, 1992, “ARCH Modelling in Finance,” Journal of Econometrics, 52, pp.5-59.
[3]Claudio Morano, 2001, “A semiparametric approach to short-term oil price forecasting,” Energy Economics, Vol.23, Issue 3, pp.325-338.
[4]Dickey, D. A. and W. A. Fuller, 1979, “Distribution of the Estimators for Autoregression Time Series with a Unit Root,” Journal of American Statistical Association, 74, pp.427-431.
[5]Dickey, D. A. and W. A. Fuller, 1981, “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root,” Econometrica, Vol49, No. 4.
[6]Ding, Z. and Engle R. F., 2001, “Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing,” Academia Economic Papers, 29, pp.157-184.
[7]Dana Van Wagener, 2014, “U.S. tight oil production: Alternative supply projections and an overview of EIA’s analysis of well-level data aggregated to the country level”, http://www.eia.gov/forecasts/aeo/tight_oil.cfm
[8]Engle, R. F., 1982, “Autoregressive Conditional Heteroscedasticity with Estimates of theVariance of United Kingdom Inflation,” Econometrica, 50, pp.987-1007.
[9]Engle, R. F. and K. F. Kroner, 1995, “Multivariate Simultaneous Generalized ARCH,” Economietric Theory, 11, pp.122-150.
[10]Engle, R. and K. Sheppard, 2001, “Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH,” Department of Economics, University of California, San Diego, Working Paper.
[11]Engle, R., 2002, “Dynamic Conditional Correlation- A simple class of multivariate GARCH models,” Journal of Business and Economic Statistics, Vol.20, No.3, pp.339-350.
[12]Granger, C. W. J. and P. Newbold, 1974, “Spurious Regression in Econometrics,” Journal of Econometrics, 2, pp.111-120
[13]Glosten, L. R., Jagannathan, R., and Runkle, D. E., 1993, “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,” The Journal of Finance, Vol.48, Issue 5, pp.1779-1801.
[14]Hassan Mohammadi, 2010, “International evidence on crude oil price dynamics: Application of ARIMA-GARCH models,” Energy Economics, Vol.32, Issue 5, pp.1001-1008.
[15]Huang, B. N., M. J. Huang, and H. P. Peng, 2005, “The assymetry of the impact of oil price shocks on economic activities: An application of the multivariate threshold model,” Energy Economics, 27, pp.455-476.
[16]Kmenta, J., 1986, Elements of Econometrics. 2nd ed., New York: Macmillan Publishing Co.