由於目前對於股價指數是否為單根的實證研究文章尚未一致性的結論，所以本文採用1999年1月至2014年12月OECD中20個國家的股價指數月資料對此議題進行分析。現今經濟事件的發生對於各國經濟變數皆會造成的衝擊，因此利用Lee et al. (2015)發展出的以傅立葉函數捕捉結構性變化且跨個體相關的BCIPS檢定，加入過去IPS檢定及CIPS檢定模型中未考慮的結構性變化，且改善以虛擬變數估計結構性變動點的不易性，讓實證研究的可行性增加。
實證結果得知，以傳統單根檢定得到的結論為大部分國家皆為接受單根；而利用追蹤資料單根檢定，不論有無加入跨個體相關的IPS檢定及CIPS檢定皆可得到接受虛無單根假設。最後以考慮結構性變化及跨個體相關的BCIPS檢定則得到拒絕虛無單根假設的相反結果，由此了解20個OECD國家中的部分國家之股價指數應是會受到經濟社會事件的衝擊影響是具有預測性的。

There is still no consistent conclusion about whether the stock price index is unit-root or not, so this paper uses stock price index month data of 20 countries in OECD from Jan, 1991 to Dec, 2014 to discuss this topic. Because the economic activities will shock the economic variables of every country, this paper applies BCIPS panel unit-root test proposed by Lee et al. (2015) that allows for smoothing structural changes modeled by Fourier function and cross-sectional dependence. This test modified IPS test and CIPS test and improve the complexity by using dummy variable to capture structural breaks.
The empirical result about stock price index shows that most of countries accept the null hypothesis of unit-root by using the traditional unit-root tests. Furthermore, IPS and CIPS test also accept the null hypothesis of unit-root. However, the result is different by applying the BCIPS panel unit-root test, it rejects the null hypothesis of unit-root. So economic and social shocks would affect the stock price index of some of 20 countries and their stock price indexes are predicable.

論文審定書 i
公開授權書 ii
謝辭 iii
摘要 iv
Abstract v
目錄 vi
圖次 viii
表次 ix
1 緒論 1
1.1 研究動機及目的 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 文獻回顧 4
2.1 單根檢定模型的回顧 . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 DF單根檢定模型 . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 ADF單根檢定模型 . . . . . . . . . . . . . . . . . . . . . . 5
2.1.3 PP單根檢定模型 . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.4 KPSS單根檢定模型 . . . . . . . . . . . . . . . . . . . . 7
2.1.5 IPS追蹤資料單根檢定 . . . . . . . . . . . . . . . . . . . 8
2.1.6 CIPS追蹤資料單根檢定 . . . . . . . . . . . . . . . . . . 9
2.1.7 LM追蹤資料單根檢定允許變動點 . . . . . . . . . . . 11
2.2 股票價格相關實證文獻 . . . . . . . . . . . . . . . . . . . . 12
3 研究方法 15
3.1 模型介紹 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 多因子單根檢定 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 以BCADF為基礎的追蹤資料單根檢定 . . . . . . . . . . . . 19
3.4 具序列相關的殘差項 . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 選擇傅立葉頻率k及落後期數p之方法 . . . . .. . . . . . . 21
4 實證結果分析 22
4.1 資料來源與說明. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 單根模型的選擇. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.1 傳統單根檢定結果. . . . . . . . . . . . . . . . . . . . . . 25
4.2.2 追蹤資料單根檢定結果 . . . . . . . . . . . . . . . . . . 27
5 結論 29
參考文獻 31
附錄 35

中文部分:
1.王孟倫，2013。消費-所得比的定態性實證分析-以OECD國家為例。高雄市，國立中山大學經濟學研究所碩士論文。
2.李慶男，2006。時間數列講義 Chapter 21。高雄市，國立中山大學經濟學研究所。
3.俞佳芬，2006。亞洲新興市場股價指數效率性檢定-運用考慮多重結構性轉變點之縱橫單根檢定法。新北市，私立淡江大學財務金融學系碩士論文。
4.陳姩彣，2013。考慮平滑性變化的實質GDP定態性-OECD國家實證研究。高雄市，國立中山大學經濟學研究所碩士論文。
英文部分:
1. Bai, J. and Carrion-i-Silvestre, 2009. Structural changes, common stochastic trends, and unit roots in panel data. The Review of Economic Studies Vol. 76, No. 2, pp. 471-501.
2. Balvers, R.,Wu, Y. and Gilliland, E., 2000. Mean reversion across national,stock markets and parametric contrarian investment strategies. The Journal of Finance Vol. 80, No. 2, pp. 745-772.
3. Becker, R., Enders, W. and Hurn, S., 2004. A general test for time dependence in parameters. Journal of Applied Econometrics Vol. 19, pp. 899-906.
4. Becker, R., Enders, W. and Lee, J., 2006. Stationarity test in the presence of an unknown number of smooth breaks. Journal of Time Series Analysis Vol. 27, pp. 381-409.
5. Carrion-i-Silvestre et al., 2005. Breaking the panels: An application to the GDP per capita. The Econometrics Journal Vol. 8, pp. 159-175.
6. Chaudhuri, K. and Wu, Y., 2003. Random walk versus breaking trend in stock prices: Evidence from emerging markets. Journal of Banking and Finance Vol.
27, pp. 575-592.
7. Chaudhuri, K. and Wu, Y., 2004. Mean reversion in stock Prices: Evidence from emerging markets. Managerial Finance Vol. 29, pp. 22-31.
8. Choudhry, T., 1997. Stochastic trends in stock prices: Evidence from latin American markets. Journal of Macroeconomics Vol. 19, pp. 285-304.
9. De Bondt W.F.M. and Richard Thaler, 1985. Does the stock market overreact? Journal of Finanace Vol. 40, No. 3, pp. 793-805.
10. Eickmeier, S., 2009. Comovements and heterogeneity in the Euro area analyzed in a nonstationary dynamic factor model. Journal of Applied Econometrics Vol. 24, pp. 933-959.
11. Enders, W. and Lee, J., 2012a. A unit root test using a Fourier series to approximate smooth breaks. Oxford Bulletin of Economics and Statistics Vol. 74, pp. 574-599.
12. Enders, W. and Lee, J., 2012b. The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters Vol. 117, pp. 196-199.
13. Engle, R.F., 1982. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica Vol. 50, No. 4, pp. 987-1007.
14. Fama, 1970. Ecient Capital Markets: A review of theory and empirical work.The Journal of Finance Vol. 25, No. 2, pp. 383-417.
15. Fama and French, K.R., 1998. Permanent and temporary components of stock prices. Journal of Political Economy Vol. 96, No. 2, pp. 246-273.
16. Im, K.S., Pesaran, M.H. and Shin, Y.C., 2003. Testing for unit roots in heterogeneous panels. Journal of Econometrics Vol. 115, pp. 53-74.
17. Im, K.S., Lee, J. and Tieslau, M., 2005. Panel LM unit-root tests with level shifts. Oxford Bulletin of Economics and Statistics Vol. 67, pp. 393-419.
18. Im, K.S., Lee, J. and Tieslau, M., 2010. Panel LM Unit root tests with trend shifts. working paper.
19. Kawakatsu H., 1999. An empirical examination of Financial liberalization and the efficiency of emerging market stock prices. The Journal of Financial Re-
search Vol. 22, No. 4, pp. 385-411.
20. Lean, H.H. and Smyth, R., 2005. Do asian stock markets follow A random walk? Evidence from LM unit root tests with one and two structual breaks. ABERU Discussion Paper 11.
21. Lee, C.C., Lee, J.D. and Lee, C.C., 2010. Stock prices and the efficient market hypothesis: Evidence from a panel stationary test with structural breaks. Japan and the World Economy Vol. 22, pp. 49-58.
22. Lee, C.N., Wu, J.L. and Yang, L.X., 2015. A simple panel unit-root test with smooth breaks in the presence of a multifactor error structure. Oxford Bulletin of Economics and Statistics Accepted.
23. Lee, J. and Strazicich, M.C., 2003. Minimum lagrange multiplier unit root test with two structural breaks. The Review of Economics and Statistics Vol. 85, No. 4, pp. 1082-1089.
24. Leybourne, S., Mills, T. and Newbold, P., 1998. Spurious rejections by Dickey-Fuller test in the presence of a break under the null. Journal of Econometrics Vol. 87, pp. 191-203.
25. Lo, A.W. and MacKinlay C., 1998. Stock market prices do not follow random walks: Evidence from a simple specification test. The Review of Financial Studies Vol. 1, No. 1, pp. 41-66.
26. McQueen, G., 1992. Long-Horizon Mean-Reverting stock prices revisited. The Journal of Financial and Quantitative Analysis Vol. 27, No. 1, pp. 1-18.
27. Narayan, P.K. and Smyth, R., 2005. Are OECD stock prices characterized by a random walk? Evidence from sequential trend break and panel data models. Applied Financial Economics Vol. 15, pp. 547-556.
28. Narayan, P.K. and Smyth, R., 2007. Mean reversion versus random walk in G7 stock prices evidence from multiple trend break unit root tests. Int. Fin. Markets, Inst. and Money Vol. 17, pp. 152-166.
29. Narayan, P.K. and Narayan, S., 2007. Mean reversion in stock prices: new evidence from panel unit root tests. Studies in Economics and Finance Vol. 24, Iss. 3, pp. 233-244.
30. Narayan, P.K., 2008. Do shocks to G7 stock prices have a permanent effect? Evidence from panel unit root tests with structural change. Mathematics and Computers in Simulation Vol. 77, pp. 369-373.
31. Pesaran, Smith, V. and Takashi Yamagata, 2013. Panel unit root tests in the presence of a multifactor error structure. Journal of Econometrics Vol. 175, pp. 94-115.
32. Poterba, J.M. and Summers, L.H., 1988. Mean reversion in stock price: Evidence and implication. The Journal of Financial Economics Vol. 22, pp. 27-59.