本篇論文考慮了高階動差性質，使用偏斜一般化誤差分配(SGED)來解釋高峰、厚尾與偏態(skewness)的金融市場資料形態，與一般常用常態分配、Student-t分配與一般化誤差分配(GED)等對稱分配進行模型績效比較，探討商品報酬率普遍存在高峰、厚尾現象時，何種分配的模型對於波動率具有較佳的相對預測能力。
本文的實證分析研究步驟如下：首先，對資料進行敘述性統計，得知應加入GARCH效果，接著透過階次篩選出最佳階次。再來，對資料做全樣本的參數估計，選出最佳模型。最後，進行樣本外估計後，分別做出1天、2天、5天、10天、20天的波動性預測，並採用不同的損失方程式評估預測的績效，來決定最佳模型的選取。再者，使用DM檢定來呈現在不同誤差分配下的模型之間的相對預測能力比較。

This paper considers the high-moments and uses the skew generalized error distribution (SGED) to explain the financial market data which have leptokurtic, fat-tailed and skewness. And we compare performance with the commonly used symmetrical distribution model such as normal distribution, student’s t distribution and generalized error distribution (GED). To research when returns of asset have leptokurtic and fat-tailed phenomena, what model has better predictive power for volatility forecasting?
The empirical procedure is as follows: First step, make the descriptive statistics of raw data, and know that the GARCH effect should be considered, followed by selecting the optimal order of ARMA-GARCH. The second steps, make the parameter estimations of full-sample, and pick up the best model. Finally, forecast out-of-sample volatility for 1-day, 2-day, 5-day, 10-day and 20-day respectively, not only use different loss function to measure the performance, but also use DM test to compare the relative predictive power of the models under the different error distribution.

論文審定書 i
誌　謝 ii
摘　要 iii
Abstract iv
1. Introduction 1
1.1 Motivations 1
1.2 Importance of metal, oil and agricultural product markets 2
2. Literature Review 7
3. Methodology 12
3.1 Time-series forecasting 12
3.2 Student’s t Distribution 13
3.3 General Error Distribution 13
3.4 Skew Generalized Error Distribution 14
3.5 Forecasting methodology 15
4. Empirical results 19
4.1 Data and descriptive statistics 19
4.2 Order selection of ARMA-GARCH 23
4.3 Full sample estimation 28
4.4 Out-of-sample forecast evaluation 32
5. Conclusions 46
References 48

Abdallah Fayyad, & Kevin Daly. (2010). “The Volatility of Market Returns: A Comparative Study of Emerging versus Mature Markets”. International Journal of Business and Management, 5, 7
Agnolucci, P. (2009). “Volatility in crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models”. Energy Economics, 31, 2, 316-321.
Alizadeh, S., Brandt, M. W., & Diebold, F. X. (January 01, 2002). “Range-Based Estimation of Stochastic Volatility Models”. The Journal of Finance, 57, 3, 1047-1091.
Bali, T. G., Tang, Y., & Mo, H. (2008). “The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR”. Journal of Banking and Finance, 32, 2, 269-282.
Bhattacharyya, M., Kumar, M. D., & Kumar, R. (2009). “Optimal sampling frequency for volatility forecast models for the Indian stock markets”. Journal of Forecasting, 28, 1, 38-54.
Brooks, C., & Persand, G. (2003). “Volatility forecasting for risk management”. Journal of Forecasting, 22, 1, 1.
Cheng, W.-H., & Hung, J.-C. (2011). “Skewness and leptokurtosis in GARCH-typed VaR estimation of petroleum and metal asset returns”. Journal of Empirical Finance, 18, 1, 160-173.
Chorro, C., Guegan, D., & Ielpo, F. (2010). “Option pricing for GARCH-type models with generalized hyperbolic innovations”. Quantitative Finance, 1-16.
Franses, P. H., & Dijk, D. V. (1996). “Forecasting Stock Market Volatility Using (Non-linear) Garch Models”. Journal of Forecasting, 15, 3, 229.
Geman, H. (2002). “Pure jump Levy processes for asset price modeling”. Journal of Banking & Finance, 26, 7, 1297.
Hansen, P. R., & Lunde, A. (2005). “A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH (1,1)?”. Journal of Applied Econometrics, 20, 7, 873-890.
John, H. A. W. (1998). “Value At Risk When Daily Changes In Market Variables Are Not Normally Distributed”. Journal of Derivatives, 5, 3,9-19.
Kang, S. H., Kang, S.-M., & Yoon, S.-M. (2009). “Forecasting volatility of crude oil markets”. Energy Economics, 31, 1, 119-125.
Kroner, K. F., Kneafsey, K. P., & Claessens, S. (1995). “Forecasting volatility in commodity markets”. Journal of Forecasting, 14, 2, 77-95.
Madan, D. B., Carr, P. P., & Chang, E. C. (1998).” The Variance Gamma Process and Option Pricing”. European Finance Review, 2, 1, 79.
Marzo, M., & Zagaglia, P. (2010). “Volatility forecasting for crude oil futures”. Applied Economics Letters, 17, 16, 1587-1599.
Patton, A. J. (2011). “Volatility forecast comparison using imperfect volatility proxies”. Journal of Econometrics, 160, 1, 246-256.
Webby, B., Boland, J., Howlett, P., & Metcalfe, A. (2009). “Tracking a rainfall index constrained by Conditional Value-at-Risk”. Anziam Journal, 51.
Wei, Y., Wang, Y., & Huang, D. (2010). “Forecasting crude oil market volatility: Further evidence using GARCH-class models”. Energy Economics, 32, 6, 1477-1484.
Wilhelmsson, A. (2009). “Value at Risk with time varying variance, skewness and kurtosis-the NIG-ACD model”. Econometrics Journal, 12, 1, 82-104.
Young, S. K., Rachev, S. T., Bianchi, M. L., Mitov, I., & Fabozzi, F. J. (2010). “Time series analysis for financial market meltdowns”. Preprint submitted to Journal of Banking and Finance.