Basic Search / Detailed Display

Author: 蕭智⽂
Chih-Wen Hsiao
Thesis Title: 運用異質變異數與精確估計模型方法分析複雜的金融時間序列數據— 以新冠疫情前後台灣股價指數期貨為例
Heterogeneity of complex financial time series data and an accurate estimation modeling approach - An example of Taiwan stock index futures before and during COVID-19
Advisor: 盧希鵬
Hsi-Peng Lu
Committee: 盧希鵬
Hsi-Peng Lu
Yi-Hsien Wang
Shih-Jhen Huang
Yen-Hsien Lee
Chih-Yu Chin
Mei-Yu Lee
Degree: 博士
Department: 管理學院 - 管理研究所
Graduate Institute of Management
Thesis Publication Year: 2022
Graduation Academic Year: 110
Language: 中文
Pages: 89
Keywords (in Chinese): ⼈工智慧異質變異數模型形式選擇複雜的⾦融數據
Keywords (in other languages): Artificial Intelligence, Heteroscedasticity, Model Form Selection, Complex Financial Data
Reference times: Clicks: 201Downloads: 0
School Collection Retrieve National Library Collection Retrieve Error Report
  • 大數據分析和人工智慧已是當前的科技主流,然而從研究方法角度解析「累加性數字」的方法較少被提及,因此,本研究提供了一種利用異質變異數估計的數學方法,以達到為複雜金融數據建立更精確的數學模型之目的。透過特定或多種數學模型的建構,由AI判斷最佳的模型,包含 (1.)運用AI,針對特定線性或非線性模型,進行資料數量的決策(AI多線段法),以及 (2.) 運用AI,從多種數學模型當中抉擇出最佳模式。後者須同時考量期望值模型和變異數異質性模型,並能合併二者以達到研究人員所能做到之最佳數學模式。同時,以新冠肺炎前後期間,台灣股價指數期貨日收益率為例。研究發現人工智慧可建構更為符合數據之數學模型,並以數學式提供良好訊號,做決策依據使用。若使用AI多線段法,則可對應上該期間市場發生的事件。若使用AI判斷多種數學模型,則可在無人為干預或設定下,符合人工智慧特性,甚至做到人類無法計算的精確數學模型結果。即使是黑天鵝的新冠肺炎事件,在本研究之分析方法上,亦得到非常良好的結果。

    Big data analysis and artificial intelligence are the current mainstream of science and technology, but the method of analyzing additive numbers from the perspective of research methods is rarely mentioned. Therefore, this study provides a method of building a more accurate mathematical model for complex financial data by using heterogeneous variance estimation. This research uses the daily yields of Taiwan Stock Index Futures as the source of raw data and focuses on analyzing three distinct time frames: before COVID-19, during COVID-19, and the entire time period. There are two methods used, and both involve AI: an AI multi-line segment method followed up with mathematical models selected by AI. AI multi-line segment method uses either a specific linear or nonlinear model fitted with optimal data quantity determined by AI. Followed up by a mathematical model selection method where AI screens for the best model from a variety of mathematical models. The latter must consider both the expected value model and the variance heterogeneity model and combine the two to achieve the goal of a more accurate mathematical model. When the AI multi-line method is used, trends and turning points coincidentally corresponds to previous events of significant impact. On the flip side, having AI decide on the two mathematical models used, out of a pool of prospects, meet the characteristics of artificial intelligence without human intervention or setting. It is found that artificial intelligence is capable of selecting more suitable mathematical models based on the characteristics of the inputted raw data. As the results are derived from a mathematical formula, it is free of manipulation and advantageous for decision-making. In addition, the result also shows higher accuracy that cannot be calculated by humans. Even during a black swan event such as the COVID-19 pandemic, this method has achieved highly accurate results.

    目錄 中文摘要 I 英文摘要 II 致 謝 III 目 錄 IV 圖 目 錄 VI 表 目 錄 VII 第一章 緒 論 1 1.1 研究背景與動機 1 1.2 研究問題與目的 5 1.3 研究流程 6 第二章 文獻探討 8 2.1 模型建構相關文獻 8 2.2 傳染病爆發對經濟之影響 11 2.3 COVID-19疫情對經濟之影響 14 2.4 小結 17 第三章 研究設計 18 3.1 研究架構 18 3.2 樣本期間與樣本選取 20 3.3 AI人工智能多線段法 22 3.4 期望值模型 24 3.5 異質變異數模型 27 3.6 具有異質變異數的期望值模型 31 第四章 實證結果與分析 33 4.1 AI人工智能多線段法 34 4.2 期望值配適模型 43 4.3 異質變異數配適模型 50 4.4 具有異質變異數的期望值配適模型 57 第五章 結論與建議 63 5.1 研究結論 63 5.2 研究建議 65 5.3研究限制 66 參考文獻 67 附錄 73 圖目錄 圖1.1 研究流程圖 7 圖3.1 研究架構圖 19 圖3.2 AI人工智能多線段法的流程圖 23 圖4.1 線性迴歸估計線圖 35 圖4.2 AI人工智能多線段法的直線線段估計線圖 36 圖4.3 AI人工智能多線段法的直線線段估計線分段圖 38 圖4.4 AI人工智能多線段法的非線性線段估計線圖 39 圖4.5 個案1實際值與配適圖 46 圖4.6 個案2實際值與配適圖 47 圖4.7 個案3實際值與配適圖 48 圖4.8 個案1異質變異數的配適殘差結果圖 53 圖4.9 個案2異質變異數的配適殘差結果圖 54 圖4.10 個案3異質變異數的配適殘差結果圖 55 圖4.11 個案1具有異質變異數的期望值配適模型圖 60 圖4.12 個案2具有異質變異數的期望值配適模型圖 61 圖4.13 個案3具有異質變異數的期望值配適模型圖 62 表目錄 表4.1 敘述性統計 33 表4.2 新冠病毒開始發生期間AI人工智能多線段法直線估計式 37 表4.3 新冠病毒開始發生期間AI人工智能多線段法非線性估計式 41 表4.4 期望值曲線迴歸係數 45 表4.5 解釋變數的曲線係數 52


    1. 王冠先, &李玫郁(2020),統計學不能做為大數據分析的工具,第1版。台北: 機統出版社。
    2. 王冠先, &李玫郁(2020),預測股價指數專案計畫,
    3. 徐康寧(2020),疫情影響下的世界經濟:變局與重塑,華南師範大學學報 (社會科學版),5,25-36。
    4. 徐煜錡、徐嘉妤、康鶴耀 (2020),新型冠狀病毒流行前後之台灣加權股價指數預測模型,創新與經營管理學刊,9(2),39-64。
    5. 張志勇、廖文華、石貴平、王勝石、游國忠(2020)。人工智慧。台北市:全華圖書。
    6. 劉栩憬, & 蘇志雄. (2021). 新冠肺炎 (COVID-19) 對台灣股價影響之探討,數據分析, 16(2), 1-19。
    7. 羅庚辛, 藍宇文, & 張尚原. (2007),台指選擇權市場最適波動度指標之研究, 風險管理學報, 9(2), 123-147。
    8. Keller, 顏慧、丁淑方譯,(2019), 統計學:基礎與應用11/e。台北:東華出版。

    9. Albulescu, C. (2020). Coronavirus and financial volatility: 40 days of fasting and fear. arXiv preprint arXiv:2003.04005.
    10. Albulescu, C. T. (2021). COVID-19 and the United States financial markets’ volatility. Finance research letters, 38, 101699.
    11. Alfaro, L., Chari, A., Greenland, A. N., & Schott, P. K. (2020). Aggregate and firm-level stock returns during pandemics, in real time (No. w26950). National Bureau of Economic Research.
    12. Bakas, D., & Triantafyllou, A. (2020). Commodity price volatility and the economic uncertainty of pandemics. Economics Letters, 193, 109283.
    13. Baum, C.F. (2006). An Introduction to Modern Econometrics Using Stata. Stata Press, College Station, 341.
    14. Begley, S. (2013). Flu-conomics: The next pandemic could trigger global recession. Health News Retrieved June 18, 2020.
    15. Belkin, M., Hsu, D. J., & Mitra, P. (2018). Overfitting or perfect fitting? risk bounds for classification and regression rules that interpolate. Advances in neural information processing systems, 31.
    16. Brandt, M. W., & Jones, C. S. (2006). Volatility forecasting with range-based EGARCH models. Journal of Business & Economic Statistics, 24(4), 470-486.
    17. Breusch, T. S., & Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica: Journal of the econometric society, 1287-1294.
    18. Brownlee, J. (2018). Better deep learning: train faster, reduce overfitting, and make better predictions. Machine Learning Mastery, 245–251.
    19. Contessi, S., & De Pace, P. (2021). The international spread of COVID-19 stock market collapses. Finance Research Letters, 42, 101894.
    20. Cook, R. D., & Weisberg, S. (1983). Diagnostics for heteroscedasticity in regression. Biometrika, 70(1), 1-10.
    21. Croce, M. M. M., Farroni, P., & Wolfskeil, I. (2020). When the markets get COVID: Contagion, viruses, and information diffusion.
    22. d'Ascoli, S., Sagun, L., & Biroli, G. (2020). Triple descent and the two kinds of overfitting: Where & why do they appear? Advances in Neural Information Processing Systems, 33, 3058-3069.
    23. Del Giudice, A., & Paltrinieri, A. (2017). The impact of the Arab Spring and the Ebola outbreak on African equity mutual fund investor decisions. Research in International Business and Finance, 41, 600-612.
    24. Dyhrberg, A. H. (2016). Bitcoin, gold and the dollar–A GARCH volatility analysis. Finance Research Letters, 16, 85-92.
    25. Enamul Hoque, M., Soo Wah, L., & Azlan Shah Zaidi, M. (2019). Oil price shocks, global economic policy uncertainty, geopolitical risk, and stock price in Malaysia: Factor augmented VAR approach. Economic research-Ekonomska istraživanja, 32(1), 3701-3733.
    26. Erdem, O. (2020). Freedom and stock market performance during Covid-19 outbreak. Finance Research Letters, 36, 101671.
    27. Ezekiel, M. (1924). A method of handling curvilinear correlation for any number of variables. Journal of the American Statistical Association, 19(148), 431-453.
    28. Frangakis, Constantine E., and Donald B. Rubin. "Principal stratification in causal inference." Biometrics 58, no. 1 (2002): 21-29.
    29. Glejser, H. (1969). A new test for heteroskedasticity. Journal of the American Statistical Association, 64(325), 316-323.
    30. Golden, R. M., Henley, S. S., White, H., & Kashner, T. M. (2019). Consequences of model misspecification for maximum likelihood estimation with missing data. Econometrics, 7(3), 37.
    31. Goldfeld, S. M., & Quandt, R. E. (1965). Some tests for homoscedasticity. Journal of the American statistical Association, 60(310), 539-547.
    32. Gormsen, N. J., & Koijen, R. S. (2020). Coronavirus: Impact on stock prices and growth expectations. The Review of Asset Pricing Studies, 10(4), 574-597.
    33. Hassan, T. A., Hollander, S., Van Lent, L., Schwedeler, M., & Tahoun, A. (2020). Firm-level exposure to epidemic diseases: Covid-19, SARS, and H1N1 (No. w26971). National Bureau of Economic Research.
    34. Heston, S. L., & Nandi, S. (2000). A closed-form GARCH option valuation model. The review of financial studies, 13(3), 585-625.
    35. Hsiao, C. W., Chan, Y. C., Lee, M. Y., & Lu, H. P. (2021). Heteroscedasticity and Precise Estimation Model Approach for Complex Financial Time-Series Data: An Example of Taiwan Stock Index Futures before and during COVID-19. Mathematics, 9(21), 2719.
    36. Jalloh, M. (2019). Estimating the economic impact of the 2014 Ebola virus outbreak in West Africa: an empirical approach. International Journal of Healthcare Policy, 1(1), 1-23.
    37. Jeris, S. S., & Nath, R. D. (2020). Covid-19, oil price and UK economic policy uncertainty: evidence from the ARDL approach. Quantitative Finance and Economics, 4(3), 503-514.
    38. Jonung, L., & Roeger, W. (2006). The macroeconomic effects of a pandemic in Europe-A model-based assessment. Available at SSRN 920851.
    39. Kerbs, T.M.; Soltys, N. (1963).Linear and Curvilinear Regression。 Proc. Inst. Mech. Eng., 178, 6-101–6-196.
    40. Lee, J. W., & McKibbin, W. J. (2004). Globalization and disease: The case of SARS. Asian economic papers, 3(1), 113-131.
    41. Lee, J.W.; McKibbin, W.J. Estimating the global economic costs of SARS. In Learning from SARS: Preparing for the Next Disease Outbreak—Workshop Summary; National Academy of Sciences: Washington, DC, USA, 2004.
    42. Lee, Y. M., & Wang, K. M. (2015). Dynamic heterogeneous panel analysis of the correlation between stock prices and exchange rates. Economic research-Ekonomska istraživanja, 28(1), 749-772.
    43. Liu, H., Manzoor, A., Wang, C., Zhang, L., & Manzoor, Z. (2020). The COVID-19 outbreak and affected countries stock markets response. International Journal of Environmental Research and Public Health, 17(8), 2800.
    44. Loh, E. (2006). The impact of SARS on the performance and risk profile of airline stocks. International Journal of Transport Economics, 33(3), 401–422.
    45. Ma, C., Rogers, J. H., & Zhou, S. (2020). Modern pandemics: Recession and recovery. Available at SSRN 3565646.
    46. Molnár, P. (2016). High-low range in GARCH models of stock return volatility. Applied Economics, 48(51), 4977-4991.
    47. Neumayer, E., & Plümper, T. (2007). The gendered nature of natural disasters: The impact of catastrophic events on the gender gap in life expectancy, 1981–2002. Annals of the association of American Geographers, 97(3), 551-566.
    48. Nuber, C., Velte, P., & Hörisch, J. (2020). The curvilinear and time‐lagging impact of sustainability performance on financial performance: Evidence from Germany. Corporate Social Responsibility and Environmental Management, 27(1), 232-243.
    49. Phan, Dinh Hoang Bach, and Paresh Kumar Narayan. "Country responses and the reaction of the stock market to COVID-19—A preliminary exposition." Emerging Markets Finance and Trade 56, no. 10 (2020): 2138-2150.
    50. Ramelli, S., & Wagner, A. (2020). What the stock market tells us about the consequences of COVID-19. Mitigating the COVID Economic Crisis: Act Fast and Do Whatever, 63.
    51. Robert F. Engle (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, The Econometric Society, 50(4), 987-1007.
    52. Ru, H., Yang, E., & Zou, K. (2020). What do we learn from SARS-CoV-1 to SARS-CoV-2: Evidence from global stock markets. Available at SSRN, 3569330.
    53. Shaeri, K., & Katircioğlu, S. (2018). The nexus between oil prices and stock prices of oil, technology and transportation companies under multiple regime shifts. Economic research-Ekonomska istraživanja, 31(1), 681-702.
    54. Siu, A., & Wong, Y. R. (2004). Economic impact of SARS: The case of Hong Kong. Asian Economic Papers, 3(1), 62-83.
    55. The World Bank. (2012). People, pathogens and our planet.
    56. Utts, Jessica M.& Heckard, Robert F. (2015), Mind on Statistics, Brooks/Cole Pub Co.
    57. Visser, M. P. (2011). GARCH parameter estimation using high-frequency data. Journal of Financial Econometrics, 9(1), 162-197.
    58. Wang, Y.-H., Yang, F.-J., Chen, L.-J. (2013). An investor’s perspective on infectious diseases and their influence on market behavior. Journal of Business Economics and Management, 14(1), 112–127.
    59. White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica: journal of the Econometric Society, 817-838.1980, 48, 817–838.
    60. Zaffaroni, P. (2009). Whittle estimation of EGARCH and other exponential volatility models. Journal of econometrics, 151(2), 190-200.
    61. Zhang, C., Vinyals, O., Munos, R., & Bengio, S. (2018). A study on overfitting in deep reinforcement learning. arXiv preprint arXiv:1804.06893.
    62. Zhang, Dayong, Min Hu, and Qiang Ji. "Financial markets under the global pandemic of COVID-19." Finance research letters 36 (2020): 101528.