中文摘要
由於資產報酬隨時間變化且具有高度持續性的特徵，因此，本文的目的在於利用隨機性波動模型，將資料進行轉換，再將命題轉為檢定該轉換後資料是否為一非恆定的序列。然而這樣的命題存有低檢力和型一誤差扭曲的問題，於是，利用模擬方式，找出穩健的檢定統計量。最後，利用實際的資料，考慮十二個國家之股票市場每日的收盤價之時間序列，搭配具有穩健型一誤差和高檢力的單根檢定量進行檢定。實證結果發現，考慮修正後的檢定統計量確實可以產生較具信賴程度的檢定結果，以那斯達克綜合股價指數和紐約史坦普爾500指數為例，其波動呈現出非恆定狀態，而新加坡海峽指數和泰國SET股價指數情況相反，其波動為一恆定序列。

Abstract
The volatility of asset returns is time varying and highly persistent. Accordingly, the purpose of this paper is to use stochastic volatility model and to test for non-stationary of the volatility process by testing a unit root in the log-squared time series. However, this may suffer from two problems - low power and severe size distortions. Owing to the consequences, we take a class of modified tests into consideration and use Monte-Carlo experiments in order to find some robust tests which have favorable size and power gains. Finally, in applying these tests to stock returns, the empirical results find that these tests about Nasdaq Composite Index and New York - S&P 500 Index do not reject the hypothesis of non-stationary stochastic volatility process. On the other hand, to take Singapore – Straitrs Index and Bangkok – Set Index for example, strong rejections of non-stationarity in volatility are obtained.

目　錄

第一章 　緒論　　　　　………………………………………………………………1
第一節 研究動機與目的　　　　　………………………………………………1
第二節 研究架構 ………………………………………………………………2
第二章 　文獻回顧　　　　　…………………………………………………………4
第一節 　隨機性波動模型之相關文獻　　　　　…………………………………4
第二節 　單根檢定之相關文獻　　　　　…………………………………………5
第三節 資產報酬之相關文獻　　　　……………………………………………7
第三章 研究方法　　　　　……………………………………………………………9
第一節 模型的建立　　　　　……………………………………………………9
第二節 相關檢定量　　　　　..…………………………………………………10
第四章 　蒙地卡羅實驗結果　　　　　………………………………………………18
第一節 型一誤差的模擬　　　　　.…………………………………………… 19
第二節 型一誤差調整後檢力的模擬　　　　　.……………………………….22
第五章 實證結果　　　　　...………………………………………………………….26
第一節 資料說明　　　　　.…………………………………………………….26
第二節 實證結果分析　　　　　………………………………………………..27
第六章 　結論　　　　　………………………………………………………………29
參考文獻　　　　　……………………………………………………………………..30


圖 目 錄

圖一 股票價格指數之波動圖形　　　　　………………………………………47


表 目 錄

表一 MAIC單根檢定之型一誤差模擬結果，以MA為例　　……………………..34
表二 BIC單根檢定之型一誤差模擬結果，以MA為例　　……………….…….35
表三 AIC單根檢定之型一誤差模擬結果，以MA為例　　……………………. 36
表四 MAIC單根檢定之型一誤差模擬結果，以AR為例　　……………………37
表五 BIC單根檢定之型一誤差模擬結果，以AR為例　　………………………38
表六 AIC單根檢定之型一誤差模擬結果，以AR為例　　………………………39
表七 MAIC單根檢定之型一誤差調整後檢力模擬結果，以MA為例　　………40
表八 BIC單根檢定之型一誤差調整後檢力模擬結果，以MA為例　　………..41
表九 AIC單根檢定之型一誤差調整後檢力模擬結果，以MA為例　　 ………..42
表十 MAIC單根檢定之型一誤差調整後檢力模擬結果，以AR為例　　…….…43
表十一 BIC單根檢定之型一誤差調整後檢力模擬結果，以AR為例　　……...44
表十二 AIC單根檢定之型一誤差調整後檢力模擬結果，以AR為例　　……...45
表十三 股票價格指數之敘述統計量　　……………………………….………….46
表十四 股票價格指數之實證結果　　……………………………….…………….49

參考文獻

[1] Andersen, T. G. and B. E. Sørensen (1996), “GMM estimation of a stochastic volatility model: a monte carlo study,” Journal of Business & Economic Statistics, 14, 328-352.
[2] Ball, C. A. and W.N. Torous (1999),“The stochastic volatility of short-term interest rates: some international evidence,” Journal of finance. LIV, No.6, 2339-2359.
[3] Danielssion, J. (1994), “Stochastic volatility in asset prices: estimation with simulated maximum likelihood,” Journal of Econometrics, 64, 375-401.
[4] Danielssin, J. and J. F. Richard (1993), “Accelerated gaussian importance sampler with application to dynamic latent variable models,” Journal of Applied Econometrics, 8, 153-173.
[5] Dickey, D. A. and W. A. Fuller (1979), “Distribution of the estimators of autoregressive time series with a unit root,” Journal of the American Statistical Association, 74, 427-431.
[6] Dufour, J. M. and M. King (1991), “Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary and nonstationary errors,” Journal of Econometrics, 47, 115-143.
[7] Elliott, G., T. J. Rothenberg and J.H. Stock (1996), “Efficient tests for an autoregressive unit root,” Econometrica, 64, 813-836.
[8] Engle, R.F. (1982), “Autoregressive Conditional heteroskedasticity with estimates of the variance of United Kingdom inflation,” Econometrica, 50, 987-1008.
[9] Engle, R. F. and T. Bollerslev (1986a), “Modelling the persistence of conditional variances,” Econometric Reviews, 5, 1-50.
[10] Engle, R. F. and T. Bollerslev (1986b), “Modelling the persistence of conditional variances: a reply,”Econometric Reviews, 5, 81-87.
[11] Ferreira, M. A. (2000), “Testing Models of the spot interest rate volatility,” Working paper, University of Wisconsin-Madison.
[12] Hansen, B. E. (1995), “Regression with nonstationary stochastic volatility,” Econometrica, 63, 1113-1132.
[13] Harvey, A. C. and N. Shephard (1993), “Estimation and testing of stochastic variance models,” Econometrics discussion paper EM/93/268, London School of Economics.
[14] Harvey, A. C. and N. Shephard (1996), “Estimation of an asymmetric stochastic volatility model for asset returns,” Journal of Business and Economic Statistics, 14, 429-434.
[15] Harvey, A. C., E. Ruiz and N. Shephard (1994), “Multivariate stochastic variance models,” Review of Economic Studies, 61, 247-264.
[16] Hsieh, D. A.(1991), “Chaos and nonlinear dynamics: application to financial markets,” Journal of Finance, 46, 1839-1877.
[17] Hull, J. and A. White (1987), “The pricing of potions on assets with stochastic volatilities,” Journal of Finance, 42,281-300.
[18] Kim, S., N. Shephard and S. Chib (1998), “Stochastic volatility: likelihood inference and comparison with ARCH models,” The Review of Economic Studies, 65, 361-393.
[19] Melino, A. and S. Turnbull (1990), “ Pricing foreign currency options with stochastic volatility,” Journal of Econometrics, 45, 239-265.
[20] Nelson, Daniel B. (1991), “Conditional heteroskedasticity in asset returns: a new approach,” Econometrica, 59, 813-836.
[21] Perron, P. and S. Ng (1995), “Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag,” Journal of the American Statistical Association, 90, 268-281.
[22] Perron, P. and S. Ng (1996), “Useful modifications to some unit root tests with dependent errors and their local asymptotic properties,” Review of Economic Studies, 63, 435-463.
[23] Perron P. and S. Ng (2001), “Lag length selection and the construction of unit root tests with good size and power,” Econometrica, 69, 1519-1554.
[24] Phillips, P.C.B. (1987), “Time series regression with unit roots,” Econometrica, 55, 277-302.
[25] Phillips, P.C.B. and Perron, P. (1988), “Testing for a unit root in time series regression,” Biometrika, 75, 335-346.
[26] Ruiz, E. (1994), “Quasi-maximum likelihood estimation of stochastic volatility models,” Journal of Econometrics, 63, 289-306.
[27] Said, S. E. and D. A. Dickey (1984), “Testing for unit roots in autoregressive-moving average models of unknown order,” Biometrika, 71, 599-607.
[28] Sandmann, G. and S. J. Koopman (1998), “Estimation of stochastic volatility models via monte carlo maximum likelihood,” Journal of Econometrics, 87, 271-301.
[29] Smith, D. R. (2002), “Markov-switching and stochastic volatility diffusion models of short-term interest rates,” Journal of Business and Economic Statistics, 20, 183-197.
[30] Taylor, S. J. (1986), “Modelling financial time series,” Chichester, U.K.: John Wiley.
[31] Taylor, S. J. (1994), “Modelling stochastic volatility: a review and comparative study,” Mathematical Finance, 4, 183-204.
[32] Weiss, A. A. (1984), “ARMA models with ARCH errors,”Journal of Time Series Analysis, 5, 129-143.
[33] Wright, J. H. (1999), “Testing for a unit root in the volatility of asset returns,” Journal of Applied Econometrics, 14, 309.