關於金融市場的價量關係，長久以來一直是研究人員所關注，過去主要是以最小平方法來研究各個金融市場的價量關係，並鮮少以大宗商品期貨市場為研究標的。本文是以分量迴歸分析法來研究美國芝加哥期貨市場（CME）玉米期貨價格與成交量之間的關係。其實證結果顯示玉米期貨之價量關係存在「價量齊揚」與「價量背離」的情況，我們分析為買賣雙方在價格上漲或下跌時，所感受到的趨勢而因應的財務行為是有差異的。此結果與傳統文獻中所運用之最小平方法所估計的迴歸模型有異，故顯示分量迴歸分析確可獲得較詳細的結論。

People always care about the relationship of price and volume in financial market. In the past the researchers used ordinary least squares (OLS) way to study the relationship and seldom apply the data of commodity market. This study was used quantile regression (QR) model to test the price-volume relationship of CME corn futures. The empirical results show positive relationships between two factors when price goes up, and negative relationships when price goes down. We analyze the situation because buyers and sellers feel different trend when price goes up or down and take different action to sell or buy. The results of QR model is different from the results of linear regressions estimated by the OLS method.

一.英文文獻
1.Angrist, J., V. Chernozhukov and I. Fernandez-Val, "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, 74, 2, 539-63, 2006.
2.Barnes, M.L. and A.W. Hughes, "A Quantile Regression Analysis of the Cross Section of Stock Market Returns," Federal Reserve Bank of Boston,02-2, 2002.
3.Bassett Jr., G.W. and H.L. Chen, "Portfolio Style: Return-Based Attribution Using Quantile Regression," Empirical Economics, 26, 1, 293-305, 2001.
4.Buchinsky, M., "Changes in the U.S. Wage Structure 1963-1987: Application of Quantile Regression," Econometrica, 62, 2, 405-458, 1994.
5.Buchinsky, M., "The Dynamics of Changes in the Female Wage Distribution in the USA: A Quantile Regression Approach," Journal of Applied Econometrics, 13, 1, 1-30, 1998.
6.Caginalp, G., D. Porter, and V.L. Smith, "Overreactions, Momentum, Liquidity, and Price Bubbles in Laboratory and Field Asset Markets," Journal of Psychology & Financial Markets, 1, 1, 24-48, 2000.
7.Campbell, J.Y., S.J. Grossman, and J. Wang, “Trading Volume and Serial Correlation in Stock Returns,” The Quarterly Journal of Economics, 108, 4, 905-939, 1993.
8.Chernozhukov, V. and C. Hansen, "Instrumental Quantile Regression Inference for Structural and Treatment Effect Models," Journal of Econometrics, 132, 2, 2006, 491-525, 2006.
9.Chernozhukov, V. and L. Umantsev, “Conditional Value-at-Risk: Aspects of Modeling and Estimation,” Empirical Economics, 26, 1, 271-292, 2001.
10.Clark, P.K.,”A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices,” Econometrica: Journal of the Econometric Society, 41, 1, 135-155, 1973.
11.Copeland, T.E., “A Model of Asset Trading Under the Assumption of Sequential Information Arrival,” The Journal of Finance, 31, 4, 1149-1168, 1976.
12.Cornell, B., “The Relationship between Volume and Price Variability in Futures Markets,” Journal of Futures Markets, 1, 3, 303-316, 1981.
13.Eide, E. and M.H. Showalter, "The Effect of School Quality on Student Performance: A Quantile Regression Approach," Economics Letters, 58, 3, 345-350, 1998.
14.Eide, E. and M.H. Showalter, "Factors Affecting the Transmission of Earnings across Generations: A Quantile Regression Approach," The Journal of Human Resources, 34, 2, 253-267, 1999.
15.Engle, R.F. and S. Manganelli, “CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles,” Journal of Business & Economic Statistics, 22, 4, 367-381, 2004.
16.Epps, T.W., “Security Price Changes and Transaction Volumes~ Theory and Evidence,” The American Economic Review, 65, 4, 586-597, 1975.
17.Fujihara, R.A.and M. Mougoué, “An Examination of Linear and Nonlinear Causal Relationships between Price Variability and Volume in Petroleum Futures Markets,” Journal of Futures Markets, 17, 4, 1997.
18.Granger, C.W.J. and P. Newbold, "Spurious Regressions in Econometrics," Journal of Economitrics, 2, 111-120, 1974
19.Gosling, A., S. Machin, and C. Meghir, "The Changing Distribution of Male Wages in the U.K.," The Review of Economic Studies, 67, 4, 635-666, 2000.
20.Hvidkjaer, S., "A Trade-Based Analysis of Momentum," The Review of Financial Studies, 19, 2, 457-491, 2006.
21.Jegadeesh, N. and S. Titman, "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," The Journal of Finance, 48, 1, 65-91, 1993.
22.Karpoff, J.M., “The Relation Between Price Changes and Trading Volume：A Survey,” Journal of Financial and Quantitative Analysis, 22, 1, 109-126, 1987.
23.Karpoff, J.M., “Costly Short Sales and the Correlation of Returns with Volume,” Journal of Financial Research, 11, 3, 173-188, 1988.
24.Kim, S.J. and J. Sheen, “Minute-by-Minute Dynamics of the Australian Bond Futures Market in Response to New Macroeconomic Information,” Journal of Multinational Financial Management, 11, 2, 117-137, 2001.
25.Koenker, R.; G. Bassett, “Regression Quantiles,” Econometrica, 46, 1, 33-50, 1978.
26.Levin, J., "For Whom the Reductions Count: A Quantile Regression Analysis of Class Size and Peer Effects on Scholastic Achievement," Empirical Economics, 26, 1, 221-246, 2001.
27.Lee, B.S. and O.M. Rui, "The Dynamic Relationship Between Stock Returns and Trading Volume~Domestic and Cross-Country Evidence," Journal of Banking & Finance, 26, 1, 51-78, 2002.
28.Li, M.Y. and P. Miu, "A Hybrid Bankruptcy Prediction Model with Dynamic Loadings on Accounting-Ratio-Based and Market-Based Information: A Binary Quantile Regression Approach," Journal of Empirical Finance, 17, 4, 818-833, 2010.
29.Majand, M. and K. Yung, “A GARCH Examination of the Relationship between Volume and Price Variability in Futures Markets,” Journal of Futures Markets, 11, 5, 613-621, 1991.
30.Martell, T.F. and A.S. Wolf, “Determinants of Trading Volume in Futures Market,” Journal of Futures Markets, 7, 3, 233-244, 1987.
31.Meligkotsidoua, L., I.D. Vrontosb and S.D. Vrontos, "Quantile Regression Analysis of Hedge Fund Strategies," Journal of Empirical Finance, 16, 2, 264-279, 2009.
32.Miller M.H.; J. Muthuswamy and R.E. Whaley, "Mean Reversion of Standard & Poor's 500 Index Basis Changes：Arbitrage-Induced or Statistical Illusion?," The Journal of Finance, 49, 2, 479-513, 1994.
33.Monoyios, M., and L. Sarno, "Mean Reversion in Stock Index Futures Markets: A Nonlinear Analysis," The Journal of Futures Markets, 22, 4, 285-314, 2002.
34.Moosa, I.A. and P. Silvapullea, "The Price–Volume Relationship in the Crude Oil Futures Market Some Results Based on Linear and Nonlinear Causality Testing," International Review of Economics & Finance, 9, 1, 11-30, 2000.
35.Morillo, D., “Income Mobility with Nonparametric Quantiles: A Comparison of the US and Germany,” Preprint, 2000.
36.Mueller, R.E., "Public- and Private-Sector Wage Differentials in Canada Revisited," Industrial Relations, 39, 3, 375–400, 2000.
37.Tauchen, G.E. and M. Pitts, “The Price Variability-Volume Relationship on Speculative Markets,” Econometrica, 51, 2, 485-505, 1983.
38.Taylor, J.W., “A Quantile Regression Approach to Estimating the Distribution of Multiperiod Returns,” The Journal of Derivatives, 7, 1, 64-78, 1999.
39.Trede, M., "Making Mobility Visible: A Graphical Device," Economics Letters, 59, 1, 77-82, 1998.

二.中文文獻
1.王毓敏、黃瑞靜，「價量關係-台股指數期貨市場之研究」，台灣金融財務季刊，2，2，97-114，2001。
2.莊家昌、管中閔，「台灣與美國股市價量關係的分量迴歸分析」，中央研究院經濟研究所，33，4，379-404，2005。
3.游雅雯、黃柏農「美股量價因果關係之探討雙變量門檻向量自我迴歸之實證分析」，國立中正大學經濟研究所碩士論文，2005。
4.蔡垂君、李存修，「台灣股價指數與指數期貨跨市場價量訊息傳遞關係之實證研究-價格發現與價量關係」，中華管理評論，7，2，46-62，2004。