本研究旨在針對COVID-19疫情期間台灣證券交易所(TWSE)上市加權及類股指數，分別採用GARCH(1,1)、EWMA作為波動度模型，並假設常態、Student’s t、Laplace三種不同之報酬機率分配進行風險值估計，透過概似比率檢定(Likelihood Ratio Test)等指標衡量何種模型及分配下估計台灣個股風險值較佳。另外，此研究將掃描統計量應用於風險值模型之獨立性檢定，與既有的檢定方法比較其檢定能力。研究結果顯示，在COVID-19疫情期間，鋼鐵及航運類股指數選擇EWMA作為波動度模型估計風險值較佳，其餘類股選擇GARCH(1,1)或EWMA則較無明顯差異；而假設t分配與Laplace分配為報酬分配估計風險值較常態分配來得佳；風險值檢定方面，本研究亦發現掃描統計檢定在檢定風險值模型時，相較既有之Kupiec, Christoffersen檢定來得更為嚴格。

This study aims to find out which volatility and distribution model perform best during the COVID-19 pandemic. We select several TWSE listed stock indices as our target, and evaluate each specification by using Kupiec and Christoffersen Tests. Besides, we provide a new method by using scan statistics to compare with the likelihood ratio tests mentioned above. Overall, Iron & Steel Index and Shipping & Transportation Index perform better when choosing EWMA as the volatility forecasting model, and both volatility forecasting model don’t appear to be robust for other indices, and assuming Student’s t and Laplace distribution are better than the Normal distribution for estimating value-at-risk during the pandemic. Among the tests we use to evaluate the Value-at-Risk model, the scan statistics method we provided is stricter than the likelihood ratio tests.

1. Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 31(3): 307-327.
2. Campbell, S. (2005). A Review of Backtesting and Backtesting Procedures. Finance and Economics Discussion Series 2005: 1-23.
3. Chaput, E.K., Meek, J.I. and Heimer, R. (2002). Spatial analysis of human granulocytic ehrlichiosis near Lyme, Connecticut. Emerging Infectious Diseases, 8, 943–948.
4. Christoffersen, P. (1998). Evaluating Interval Forecast, International Economic Review, 3 (4): 841-862.
5. Ding, J. and Meade, N. (2010). Forecasting accuracy of stochastic volatility, GARCH and EWMA models under different volatility scenarios. Applied Financial Economics, 20(10), 771-783.
6. Echaust, K. and M. Just (2020). Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection. Mathematics 8(1): 114.
7. Galdi, F. C., & Pereira, L. M. (2007). Value at Risk (VaR) Using Volatility Forecasting Models: EWMA, GARCH and Stochastic Volatility. Brazilian Business Review, 4(1), 74–94.
8. Glaz J, Pozdnyakov V, Wallenstein S (2009) Scan Statistics Methods: and Applications. Springer
9. Huang, Y. C., & Lin, B. J. (2004). Value-at-Risk analysis for Taiwan stock index futures: Fat tails and conditional asymmetries in return innovations. Review of
Quantitative Finance and Accounting, 22, 79–95.
10. Kupiec, P. (1995). Techniques for Verifying the Accuracy of Risk Measurement Models. Journal of Derivatives 3, 73-84.
11. Lee, S. and L. Nguyen (2017). Comparative Study of Volatility Forecasting Models: The Case of Malaysia, Indonesia, Hong Kong and Japan Stock Markets. Economics World 5.
12. Morgan, J.P. (1996) Risk Metrics—Technical Document. J.P. Morgan/Reuters, New York.
13. Naus, J. (1963). Clustering of Random Points in the Line and Plane, Ph.D.
thesis, Rutgers University, New Brunswick, NJ.
14. Orhan, M. and B. Köksal (2012). A comparison of GARCH models for VaR estimation. Expert Syst. Appl. 39(3): 3582–3592.
15. Peter, D. P. (1972). The Distribution of Share Price Changes. The Journal of Business 45(1): 49-55.
16. Van Den Goorbergh, R. and P. Vlaar (1999). Value-at-Risk Analysis of Stock Returns: Historical Simulation, Tail Index Estimation? De Nederlanse Bank-Staff Report 40.
17. Ye, W., Zhu W., Miao, B. (2014). Empirical Analysis of Financial Crisis Contagion Based on Scan Statistics , Journal of Management Science & Statistical Decision 11(1): 1-12.