本研究使用相關係數隨時間變動的雙變量GARCH(1,1)模型(time-varying correlation bivariate GARCH(1,1) model)，討論台灣股票市場中，大公司與小公司之間的報酬、衝擊(shock)、波動(volatility)是否互為影響為主軸。其次，為了了解不同估計方法、相關係數的設定和解釋變數對結果造成的影響，亦設立了3種模型，作為本研究的比較模型。
本研究發現大公司與小公司過去的報酬，存在雙向的報酬外溢效果。換句話說，大公司與小公司過去的報酬分別都對「本身報酬」有影響外，對「對方的報酬」也有影響。進一步發現到：大公司過去受到的衝擊和波動不僅對本身的條件變異數造成影響，也影響到小公司的條件變異數。但相反地，小公司過去受到的衝擊和波動，只對本身的條件變異數有影響，對大公司的條件變異數沒有影響，所以大、小公司間的衝擊外溢效果和波動外溢效果有不對稱的現象。
從不同模型之比較也發現，在討論大公司與小公司的報酬及波動時，應重視兩者彼此相互影響的關係，在估計時使用多變量的方法，以捕捉彼此相依的條件共變異數及條件變異數之動態過程。除此之外，也應考量兩者的相關係數隨時間變動的特性，及過去的波動對描述對方條件變異數的重要性。

關鍵字：多變量、GARCH模型、波動性、外溢效果、不對稱性

[1] 王元章(1990)，交易量、股價波動性及波動性外溢─台灣股市之實證研究，中華財務學會1999年會暨財務金融學術論文研討會，pp.995~1016
[2] 王英明(2007)，台股報酬波動與訊息到達之關係硏究，國立政治大學國際貿易硏究所，碩士論文
[3] 郭俊宏(2004)，多變量條件變異數模型之比較分析，國立台灣大學經濟學硏究所，碩士論文
[4] Akaike(1973)，Information theory and an extension of the maximum likelihood principle. In B.N. Petrov and F. Csaki(eds.)，2nd International Symposium on Information Theory，pp.267~281
[5] Akgiray(1989)，Conditional heteroskedasticity in time series of stock returns: Evidence and forecasts，Journal of Business 62，pp.55~80
[6] B.B.Mandelbrot (1963)，The variation of certain speculative prices， The Journal of Business of the University of Chicago 36，pp.394~419
[7] Bollerslev(1986)，Generalize autoregressive conditional heteroskedasticity.，Journal of Econometrics 31，pp.307~327
[8] Bollerslev, Engle, and Wooldridge(1988)，A capital-asset pricing model with time-varying covariances，Journal of Political Economy 96，pp.116~131
[9] Bollerslev(1990)，Modelling the coherence in short-run nominal exchange rates: Multivariate generalized ARCH approach，Review of Economics and Statistics 72，pp.498~505
[10] Chelley-Steeley and Steeley(1996)，Volatility transmission in the UK equity market.，The European Journal of Finance 2，pp.145~160
[11] Chou, R. F. (1988)，Volatility persistence and stock valuations: Some empirical evidence using GARCH，Journal of Applied Econometrics 3，pp.279~294
[12] Conrad, Gultekin, and Kaul(1991)，Asymmetric predictable of conditional variances.，The Review of Financial Studies 4，pp.597~622
[13] Engle(1982)，Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflations.，Journal of Financial Economics 19，pp.987~1007
[14] Engle and Kroner(1995)，Multivariate simultaneous generalized ARCH， Econometric Theory 11，pp.122~150
[15] Engle(2002)，Dynamic conditional correlation: A simple class of multivariate GARCH models，Journal of Business and Economic Statistics 20，pp.339~350
[16] French, Schwert, and Stambaugh(1987)，Expected stock returns and volatility，Journal of Financial Economics 19，pp.3~29
[17] Glosten, Jagamnnathan, and Runkle(1993)，On the relation between the expected value and the volatility of the nominal excess return on stocks，Journal of Finance 48，pp.1779~1801
[18] Hamao,Masulis,and Ng(1990)，Correlation in price changes and volatility across international stock markets，The Review of Financial Studies，pp.281-307
[19] King and Wadhwani (1990)，Transmission of Volatility between Stock
Markets.，Review of Financial Studies 3，pp.5~33
[20] Lo and Mackinlay(1990)，When are contrarian profits due to stock market over-reaction?，Review of Financial Studies 3，pp.175~205
[21] Nelson(1991)，Conditional heteroskedasticity in asset returns: A new approach， Econometrica 59，pp.347~370
[22] Pyun, Lee, and Nam(2000)，Volatility and information flows in emerging equity market: A case of the Korean stock exchange.，International Review of Financial Analysis 9，pp.405~420
[23] Reyes(2001)，Asymmetric volatility spillover in the Tokyo stock exchange.”，Journal of Economics and Finance 25，pp.206~213
[24] Ross(1989)，Information and volatility: The no-arbitrate martingale approach to timing and resolution irrelevancy.，Journal of Finance 44，pp.1~17
[25] Schwert and Seguin(1990)，Heteroskedasticity in stock returns，Journal of Finance 45，pp.1129~1156
[26] Tse and Tsui(2002)，A multivariate GARCH model with time-varying correlations，Journal of Business & Economic Statistics 10，pp.351~362