臺灣博碩士論文加值系統

波動度預測在財務領域中是一個非常重要的議題，有許多的因子都會影響到波動度，許多研究都發現資產波動度有ARCH結構，且不同研究者提供了不同方法去描述波動度的隨機過程。本篇文章將會使用一種類神經網路方法-自組織對映，先行將市場上的資訊做事前分類，並將此分類結果帶入預設的波動度模型GJR GARCH後提供一個能捕捉波動度異常跳躍的模型。本篇論文資料使用台灣的股票資料的日內資料計算日內波動度，並發現此模型適用會有異常跳躍的股票，且平常並無太大起伏，因此本篇文章提供一個方法建議金融商品發行商在評價商品價格時，調整波動度的時機點。同時，本篇文章也建議使用Hampel Identifier 去判別一筆資料是否適用於本模型，也發現了並非所有資訊對於波動度都是正面影響，有些類別資訊可能有負面影響，而這結果與Chen, X. and Ghysels(2011)所提出只有非常好的消息或壞消息對於波動度才有影響，一般消息可能會有負面影響。本文所使用的模型，用以解決類神經相關方法在財務資料分析上無法給予有效解釋的問題，我們能夠透過類神經與計量模型結合，用以解釋模型結果。

Volatility prediction is an important issue in the financial market. Since many factors will influence the volatility, it still cannot be predicted accurately. Most research agree that the volatility process has ARCH effect, and many methods have be proposed to describe the volatility process. This paper gives a new aspect of volatility. Our work uses the self organizing map, an artificial neural network method to verify the information type and put this information into the GJR GARCH model, which proposed by Engle and Victor. By using this model, the volatility of individual stock can be predicted better than using the simple GJR GARCH model. with some type of asset. And the result of this model also has similar result with Chen and Ghysels (2011)[1], which implies that some type of information will decrease the mean of the future volatility. Our raw data is the assets’ realized volatility in Taiwan to be our data, and found that not all of the assets are suitable for this model but three assets are. Hence, in conclusion we propose a method to detect what kind of data is suitable for this model. It also gives the criteria to determine the time for changing pricing volatility. Moreover, this model gives you a methodology for testing the results given from artificial neural network.

Content
1 Introduction 8
2 Literature Review 12
2.1 Self Organizing Map 12
2.2 GJR GARCH 15
3 Methodology 17
4 Empirical Result 23
4.1 Determine ARMA order of return process 23
4.2 Stationary Test 24
4.3 Determine the residual white noise or not 26
4.4 Determine the information 29
4.5 Estimate the parameters of modified GJR-GARCH 31
4.6 Comparison of GJR GARCH and modified GJR GARCH 37
5 Conclusion 40
Reference 42
Appendix 45
A1. Maximum Likelihood Estimation 45
A2. SOM Plot of each companies 46
A3. Estimation results of GJR GARCH of each companies 51
A4. Code of MLE process within modified GJR GARCH 53
A5. Code of Wald test 60

1.Chen, X., & Ghysels, E. (2011). News—good or bad—and its impact on volatility predictions over multiple horizons. Review of Financial Studies, 24(1), 46-81.
2.Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American statistical association, 74(366a), 427-431.
3.Duan, J. C. (1995). The GARCH option pricing model.Mathematical finance,5(1), 13-32.
4.Engle, R. F., & Ng, V. K. (1993). Measuring and testing the impact of news on volatility. The journal of finance, 48(5), 1749-1778.
5.French, K. R., Schwert, G. W., & Stambaugh, R. F. (1987). Expected stock returns and volatility. Journal of financial Economics, 19(1), 3-29.
6.Glosten, L. R., Jagannathan, R., & 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, 48(5), 1779-1801.
7.Hampel, F. R. (1971). A general qualitative definition of robustness. The Annals of Mathematical Statistics, 1887-1896.
8.Hampel, F. R. (1974). The influence curve and its role in robust estimation. Journal of the American Statistical Association, 69(346), 383-393.
9.Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. The journal of finance, 42(2), 281-300.
10.Kodde, D. A., & Palm, F. C. (1986). Wald criteria for jointly testing equality and inequality restrictions. Econometrica: journal of the Econometric Society, 1243-1248.
11.Kohonen, T., Hynninen, J., Kangas, J., & Laaksonen, J. (1996). Som pak: The self-organizing map program package. Report A31, Helsinki University of Technology, Laboratory of Computer and Information Science.
12.Kohonen, T. (1998). The self-organizing map. Neurocomputing, 21(1), 1-6.
13.Keogh, E., Lin, J., & Truppel, W. (2003, November). Clustering of time series subsequences is meaningless: Implications for previous and future research. In Data Mining, 2003. ICDM 2003. Third IEEE International Conference on (pp. 115-122). IEEE.
14.Kuwahara, H., & Marsh, T. A. (1992). The pricing of Japanese equity warrants. Management Science, 38(11), 1610-1641.
15.Ljung, G. M., & Box, G. E. (1978). On a measure of lack of fit in time series models. Biometrika, 297-303.
16.Tsay, R. S., & Tiao, G. C. (1984). Consistent estimates of autoregressive parameters and extended sample autocorrelation function for stationary and nonstationary ARMA models. Journal of the American Statistical Association,79(385), 84-96.
17.Tsay, R. S. (2005). Analysis of financial time series(Vol. 543). John Wiley & Sons.