本文主要探討美國採購經理人指數（PMI）與Vanguard ETF(VTI)之間的關係，我們參考了Stock and Watson(1998、2002)利用主成分分析法(Principal Component Analysis, PCA)嘗試建立可預測美國道瓊股市指數表現的改良PMI指標，並使用PMI與透過6個領先指標建立了一個新PMI指標，在資料處理後使用了樣本內與樣本外測試來驗證方法之可行性，本文期待讀者能因本文的研究提升研究經濟景氣循環預測之效果，並做為經濟研究單位或私人研究機構之參考。

我們根據國內外投資方面的研究報告常使用之領先指標為出發點，經過篩選後將美國PMI製造業指數加入美國首次申請失業救濟金人數、新屋開工、美銀美林高收益債指數、ECRI、OECD美國領先指標與蘇富比公司股價等領先指標為因子，欲探討新創之PMI指標對美國整體股市的預測能力。另外，我們採用主成份分析法與Mean Squared Error為本研究的架構，本研究的實證結果為:

1. 以主成分分析法將領先指標構成項目差分後建立新PMI指標時，由因果檢定及相關係數可看出DNPMI和美國道瓊股市(DVTI)有顯著的正相關係數，DPMI則不顯著。

2. 以PCR建立綜合指標測試，發現在 1997~2014.10 樣本區間中，經落後期因果檢定及相關係數發現: PMI指標沒有領先VTI, 但VTI的表現領先新PMI指標; 另外,VTI和新PMI指標之間是雙向的因果關係 (但VTI領先新PMI的證據較強).
3. 我們發現在2012年以後新PMI在追蹤VTI指數效果有明顯的追蹤偏離情形，本文認為原因在於很多國家這幾年在股市方面的表現好的產業與壞產業指數差異極大，若美國股市表現不是如1998-2012年一樣由房地產與服務業當火車頭的方式來拉動股市表現的情況下，新PMI 預測能力預測效果就會受限。

關鍵詞：PMI、VTI、改良PMI、主成份分析法、因果檢定。

This paper discusses the relationship between the US purchasing manager index (PMI) and Vanguard ETF (VTI). We utilized PCA method (Principal Component Analysis), which is adopted by Stock & Watson (1998, 2002), in an attempt to establish a modified PMI index to better predict the stock market performance. A new PMI index was built with six leading indicators. In-Sample and Out-Sample test are adopted to test the feasibility of the method. By reading this study, we expect to enhance the forecast ability of the economic business cycle for economic research units or for private research institutions.

This study based on the leading indicators often used by well-known investment research reports. US initial claims for unemployment benefits, housing starts, Merrill Lynch High Yield Bond Index, ECRI Leading Indicator, OECD index for United States and Sotheby stock price (BID:US) were then added into US PMI manufacturing index to discuss the ability to predict the US stock market.

We used principal component analysis (PCA) and Mean Squared Error-based research as a framework. The empirical results of this study are as followed:
1. In principal component analysis, we used the first difference of the leading indicators to construct a new PMI indicator. In the results of the causality test and the correlation coefficient pointed out a significant positive correlation coefficient between the Modified PMI and VTI. However, such a relationship was not found with DPMI.
2. According to the comprehensive index built with PRC, between 1997 and 2014.10 sample interval, the following results have been found when making the causal correlation coefficient test: PMI does not lead VTI, instead, VTI leads PMI. In addition, there is a bi-directional causality between VTI and Modified PMI. (There is more evidence showing that VTI leads Modified PMI.)
3. There is an apparent deviation of the effect to track VTI index using Modified PMI index after 2012. The reason is because there is large difference in the stock index between the good industries and the bad industries in lots of countries in the recent years. If the US stock market performance cannot lead the stock market as in 1998-2012 when the market performance was driven by the real estate and stock service sector, the forecasting ability of the new PMI index will be limited.

Key word：PMI、VTI、Modified PMI、Principal Component Analysis、Mean Squared Error。

論文審定書…………………………………….….i
誌謝…………………………………....………….ii
中文摘要……………..…………………………..iii
英文文摘………………………………..............iv
目錄………………....…………………………...vi

第一章、緒論
1.1 研究動機…………….....….……………...1
1.2 研究範圍與限制…………...................…2
第二章、文獻探討與ETF
2.1 文獻探討……………….....…………..…..4
2.2 Vanguard TF……….............................5
2.3 領先指標構成項目…............……………7
第三章、研究方法
3.1 單根檢定(Unit Root Test)……............…9
3.2 主成份分析法…..................………..…10
3.3 最適落後檢定……………….................12
3.4 Root Mean Squared Error根均方誤…...12
3.5 Granger因果關係檢定…......................13
3.6 實證模型………..............................…14
第四章、資料蒐集與處理…….............………15
第五章、實證與結果
5.1 迴歸模型(尋找變數)……......................21
5.2 建構預測模型……......................….....21
5.3 樣本內與樣本外預測…….............…….24
第六章、結論與建議………....................…...27
附錄…………………….................................29
參考文獻……………….......................………30

中文文獻

1. 國家發展委員會經濟研究處(2000), 「我國第九次景氣循環高峰谷底之認定」, 《歷次景氣循環認定工作報告》, 1–4
2. 國家發展委員會經濟研究處(2000), 「我國第十次景氣循環高峰谷底之認定」, 《歷次景氣循環認定工作報告》,Q&A, 1–3
3. 伍偉榮(2005) , 「摩根成分股調整對現股價量的影響」, 《國立中山大學財務管理學系碩士在職專班碩士論文》, 36
4. 徐志宏、周大森(2009) , 「近期台灣景氣循環峰谷之認定」, 《行政院經建會經濟研究》, Volume 10, 9–11
5. 陸姿樺(2007) , 「成分股調整之股價效應：以摩根台指與台灣50 指數作比較」, 《政大機構典藏》, 25–29
6. 陳馨蕙、黃月盈(2013) , 「台灣製造業採購經理人指數之編制與剖析」, 《國家發展委員會經建專論Thesis》, Volume11, 66–69
7. 黃賢楨(2004) , 「景氣循環與投資策略 - 以美國市場為例」, 《政大機構典藏》, Volume, 3.1–3.18
8. 黃月盈(2012) , 「建構景氣指標方法之研析」, 《國家發展委員會經建專論Economic Research》, Volume 3, 51–53
9. 黃裕烈、徐之強(2005) , 「景氣基準循環指數之檢討與修訂」,《行政院經濟建設委員會》, 6–9
10. 顏慶章(2009) , 「金融海嘯週年的省思」,《全球工商》, 10–12

13. 黃裕烈、徐之強，“景氣基準循環指數之檢討與修訂”，行政院經濟建設委員會委，2005年
14. 顏慶章，“金融海嘯週年的省思，全球工商”，2009年

英文文獻

1. Bachman, D. (2010), “The Information Content of the ISM Purchasing Managers’ Survey,” U.S. Department of Commerce, 12–14
2. Berge, T. (2014), “Predicting Recessions with Leading Indicators: Model Averaging and Selection Over the Business Cycle”, The Federal Reserve Bank of Kansas City Research Working Papers , 12–13
3. Bordo, M. D. and Haubrich, J. G. (1996), “The Yield Curve as a Predictor of U.S. Recessions,” Current Issues in Economics and Finance, 2(7), 3–5
4. Brillinger, D. R. (1964), “The Asymptotic Behaviour of Tukey's General Method of Setting Approximate Confidence Limits (The Jackknife) When Applied to Maximum Likelihood Estimates,” International Statistical Institute, 32(3), 202–205
5. Business Cycle Dating Committee (2003) , “The NBER’s Business-Cycle Dating Prodecure,” National Bureau of Economic Research, 7–10
6. Dickey, D. A. and Fuller, W. A. (1979), “Distribution of the Estimators for Autoregressive Time Series With a Unit Root,” Journal of the American Statistical Association, 74(366), 427–430
7. Dickey, D. A. and Fuller, W. A. (1981), “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root,” Econometrica, 49(4), 1057–1061
8. Dickey, D. A. and Fuller, W. A. (1984), “The Dickey-Fuller Test Family and Changes in the Seasonal Pattern,” Annales d'Économie et de Statistique, 76–81
9. Estrella, A. and Mishkin, F. S. (1996), “The Yield Curve as a Predictor of U.S. Recessions,” Current Issues In Economics and Finance, 2(7), 3–5
10. Ferri, R. A. (2009), “The ETF Book: All You Need to Know about Exchange-Traded Funds,” ISBN: 9780470537466
11. Fritsche, U. and Kuzin, F. (2010), “Prediction of Business Cycle Turning Points in Germany,” Jahrbücher f. Nationalökonomie u. Statistik, 225(1), 4–9
12. GRANGER, C.W.J. and NEWBOLD, P. (1974), “Spurious Regressions In Econometrics,” Journal of Econometrics 2, 112–116
13. Harris, L. and Gurel, E. (1986), “Price and Volume Effects Associated with Changes in the S&P 500 List: NewEvidence for the Existence of Price Pressures,” The Journal of Finance, 41(4), 818–825
14. Harris, E. S. (1991), “Tracking the Economy with the Purchasing Managers’ Index,” FRBNY Quarterly Review, 61–69
15. Kauffman, R. G. (1999), “Indicator Qualities of the NAPM Report On BusinessⓇ”, The Journal of Supply Chain Management, 29–37.
16. Koenig, E. F. (2002) “Using the Purchasing Managers’ Index to Assess the Economy’s Strength and the Likely Direction of Monetary Policy,” Federal Reserve Bank of Dallas, 1(6), 29–37
17. Lahiri K. and Monokroussos G. (2011), “ Nowcasting US GDP: The role of ISM Business Surveys,” , Department of Economics, 650–653
18. Lindsey, M. D. and Pavur, R. J. (2005), “As the PMI Turns: A Tool for Supply Chain Managers,” Journal of Supply Chain Management, 41(1), p30–39
19. MarketLine, (2015), “ The Vanguard Group, Inc,” http://store.marketline.com/Product/the_vanguard_group_inc?productid=14D8A3E8-7661-4BB1-9942-70A8D3B74F19
20. Nawrocki, D. and Carter, W. (1996), “Phase of the USA Business Cycle and the Investment Performance of Internationally Diversified Portfolios,” 10–11
21. Peláez R. F. (2003a), “A New Index Outperforms the Purchasing Managers’ Index,” Quarterly Journal of Business & Economics, (Winter 2003), 41–55
22. Peláez R. F. (2003b), “A Reassessment of the Purchasing Managers’ Index”, Business Economics, (Fall 2003), 35–41
23. Romer, C. D. (1999), “Changes in Business Cycles: Evidence and Explanations,” NBER
24. Stock, J. H. and Watson, M. W. (1998), “Diffusion indexes,” NBER working paper 6702, 93(441), 9–11
25. Stock, J. H. and Watson, M. W. (2002), “Macroeconomic forecasting using diffusion indexes,” Journal of Business and Economic Statistics, 148–150
26. Stock, J. H. and Watson, M. W. (2006), “Why Has U.S. Inflation Become Harder To Forecast?”, NBER working paper series, 28–33
27. Taylor, J. G. (1998), “Investment Timing and the Business Cycle,” ISBN-13: 978-0471188797
28. Xie, M. (2012), “Do Vanguard ETF Investors Make Good Decisions? – Testing the Bogle Hypothesis,” Professor Edward Tower, Faculty Advisor, 7–9