本文為一實證研究，以美國標準普爾500指數 (S&P 500) 之11種市場行業指數 (market sectors index) 作為研究資料，使用自迴歸模型 (autoregressive model) 對資料進行前處理後，採用面板數據相關性檢定 (panel data correlation test) 計算出股市崩盤指標 CD-AR (autoregressive-filtered cross-sectional dependence) ，並運用相關性檢定與迴歸模型觀察以行業相關性作為建立基礎的 CD-AR 指標與整體市場報酬率之關係。研究結果顯示行業相關性與整體市場報酬率為顯著負相關，且負相關效果主要體現於股市下跌時，股市上漲時則因資金效果同漲使行業相關性與報酬率呈現正相關。接著本文透過遞迴進化演算法 (recursive evolving algorithm) 計算 CD-AR 指標變動率之最佳 Z-score ，並根據其顯著性偵測股市崩盤，成功對應至歷次著名崩盤事件。過去文獻多著重於全球市場相關性與金融危機之間的關聯，本文將研究延伸至市場行業相關性與股市崩盤之間的關聯，有助於投資人實行風險控管，以及政府監督市場與制定政策。

In this study, we make use of an AR (autoregressive)-filtered version of cross-sectional dependence test (CD-test) to construct an early warning indicator CD-AR for US market risk or crash. Since CD-AR is constructed by eleven S&P 500 market sectors index, the value of CD-AR represents the degree of sectors correlation. The empirical results show that there’s a significant negative relationship between sectors correlation and market return, and the negative correlation is more significant when we only consider negative return. Moreover, we find that the relationship become positive when we only consider positive return, one probable explanation is that the stock market is positively affected by quantitative easing (QE), moving sectors up simultaneously, and most of the positive period is dominated by the effect in the last twenty years. Based on the above results, we then test the significance of CD-AR rate Z-score by using recursive evolving algorithm, detecting the US market crash successfully. Most of the previous studies focus on the relationship between global market correlation and financial crisis, we expand the research to the relationship between sectors correlation and market crash, and our findings help exercise market surveillance, risk management, and policy action.

1.前言----------------------7
2.文獻回顧與假說建立---------12
3.資料與研究方法-------------16
4.實證結果------------------21
5.結論----------------------29
參考文獻--------------------30

1. Acharya, V. V. (2009), “A Theory of Systemic Risk and Design of Prudential Bank Regulation.” Journal of Financial Stability, 5, 224-255.
2. Baig, T. and I. Goldfajn (1999), “Financial Market Contagion in the Asian Crisis.” IMF Staff Papers, 46, 167-195.
3. Baillie, R. T. (1996), “Long Memory Processes and Fractional Integration in Econometrics.” Journal of Econometrics, 73, 5-59.
4. Bekaert, G., C. Harvey, and A. Ng (2005), “Market Integration and Contagion.” Journal of Business, 78, 39-70.
5. Bollerslev, T. and J. H. Wright (2000), “Semiparametric Estimation of Long-memory Volatility Dependencies: The Role of High-frequency Data.” Journal of Econometrics, 98, 81-106.
6. Bookstaber, R. (1997), “Global Risk Management: Are We Missing the Point?” Journal of Portfolio Management, 23, 102-107.
7. Breusch, T. S. and A. R. Pagan (1980), “The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics.” The Review of Economic Studies, 47, 239-253.
8. Calvo, S. G. and C. Reinhart (1996), “Capital Flows to Latin America: Is There Evidence of Contagion Effects?” In Guillermo Calvo, Morris Goldstein, and Eduard Hochreiter (ed.), Private Capital Flows to Emerging Markets After the Mexican Crisis, 151-171.
9. Cao, D., W. Long, and W. Yang (2013), “Sector Indices Correlation Analysis in China's Stock Market.” Procedia Computer Science, 17, 1241-1249.
10. Carrieri, F., V. Errunza, and K. Hogan (2007), “Characterizing World Market Integration through Time.” Journal of Financial and Quantitative Analysis, 42, 915-940.
11. Cheung, Y.-L. and S.-C. Mak (1992), “The International Transmission of Stock Market Fluctuation between the Developed Markets and the Asian—Pacific Markets.” Applied Financial Economics, 2, 43-47.
12. Eun, C. and S. Shim (1989), “International Transmission of Stock Market Movements.” Journal of Financial and Quantitative Analysis, 24, 241-256.
13. Forbes, K. and R. Rigobon (2001), “Measuring Contagion: Conceptual and Empirical Issues.” In Stijn Claessens and Kristin Forbes (ed.), International Financial Contagion, 43-66.
14. Forbes, K. and R. Rigobon (2002), “No Contagion, Only Interpendence: Measuring Stock Market Co-movements.” The Journal of Finance, 57, 2223-2261.
15. King, M., E. Sentana, and S. Wadhwani (1994), “Volatility and Links between National Stock Markets.” Econometrica, 62, 901-933.
16. Kose, M. A., E. Prasad, K. Rogoff, and S.-J. Wei (2009), “Financial Globalization: A Reappraisal.” IMF Staff Papers, 56, 8-62.
17. Laborda, R. and J. Olmo (2021), “Volatility Spillover between Economic Sectors in Financial Crisis Prediction: Evidence Spanning the Great Financial Crisis and Covid-19 Pandemic.” Research in International Business and Finance, 57, 101402.
18. Lee, H.-S. (2006), “International Transmission of Stock Market Movements: A Wavelet Analysis.” Applied Economics Letters, 11, 197-201.
19. Lee, J. H. H. and M. L. King (1993), “A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances.” Journal of Business & Economic Statistics, 11, 17-27.
20. Lehkonen, H. (2009), “Stock Market Integration and the Global Financial Crisis.” Review of Finance, 19, 2039-2094.
21. Lin, W.-L., R. F. Engle, and T. Ito (1994), “Do Bulls and Bears Move across Borders? International Transmission of Stock Returns and Volatility.” The Review of Financial Studies, 7, 507-538.
22. Lo, A.W. (2008), “Hedge Funds, Systemic Risk, and Financial Crisis of 2007-2008: Written Testimony for The House Oversight Committee Hearing on Hedge Funds.” MIT Working Paper.
23. Longin, F. and B. Solnik (2001), “Extreme Correlation of International Equity Markets.” The Journal of Finance, 56, 649-676.
24. Patro, D. K., M. Qi, and X. Sun (2009), “A Simple Indicator of Systemic Risk.” Journal of Financial Stability, 9, 105-116.
25. Pesaran, M. H. (2004), “General Diagnostic Tests for Cross Section Dependence in Panels.” IZA Discussion Paper, No. 1240.
26. Phillips, P. C. B. and S. Shi (2018), “Real Time Monitoring of Asset Markets: Bubbles and Crises.” Cowles Foundation Discussion Paper, No. 2152.
27. Pukthuanthong, K. and R. Roll (2009), “Global Market Integration: An Alternative Measure and its Application.” Journal of Financial Economics, 94, 214-232.
28. Sukcharoen, K. and D. J. Leatham (2016), “Dependence and Extreme Correlation among US Industry Sectors.” Studies in Economics and Finance, 33, 26-49.
29. Wang, S.-H., C. Hsiao, and H.-H. Yang (2021), “Market Integration, Systemic Risk and Diagnostic Tests in Large Mixed Panels.” Econometric Reviews, 40, 750-795.
30. Yilmaz, M. K., A. Sensoy, K. Ozturk, and E. Hacihasanoglu (2015), “Cross-sectoral Interactions in Islamic Equity Markets.” Pacific-Basin Finance Journal, 32, 1-20.