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| Title | 用馬可夫鏈蒙地卡羅法估計隨機波動模型：台灣匯率市場的實證研究 |
| Creator | 賴耀君 Lai,Simon |
| Contributor | 毛維凌 賴耀君 Lai,Simon |
| Key Words | 隨機波動模型 馬可夫鏈蒙地卡羅法 貝氏估計 適應性拒絕抽樣法 槓桿效果 厚尾分配 Gibbs sampler scale mixture Metropolis-Hastings (c) Geweke convergence diagnostic |
| Date | 2002 |
| Date Issued | 18-Sep-2009 15:52:30 (UTC+8) |
| Summary | 針對金融時序資料變異數不齊一的性質，隨機波動模型除了提供於ARCH族外的另一選擇；且由於其設定隱含波動本身亦為一個隨機波動函數，藉由設定隨時間改變且自我相關的條件變異數，使得隨機波動模型較ARCH族來得有彈性且符合實際。傳統上處理隨機波動模型的參數估計往往需要面對到複雜的多維積分，此問題可藉由貝氏分析裡的馬可夫鏈蒙地卡羅法解決。本文主要的探討標的，即在於利用馬可夫鏈蒙地卡羅法估計美元/新台幣匯率隨機波動模型參數。除原始模型之外，模型的擴充分為三部分：其一為隱含波動的二階自我回歸模型；其二則為藉由基本模型的修改，檢測匯率市場上的槓桿效果；最後，我們嘗試藉由加入scale mixture的方式以驗證金融時序資料中常見的厚尾分配。 |
| 參考文獻 | 1. Black, F. (1976). Studies of stock market volatility changes. Proceedings of the American Statistical Association, Business and Economic Statistics Section, 177-181. 2. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307-327. 3. Brooks, S. P. (1998). Markov chain Monte Carlo method and its application. The Statistician. 47, 69-100. 4. Casella, G., George, E.I., (1992). Explaining the Gibbs sampler. The American Statistician 46,167-174. 5. Cowles, M. and Carlin, B. (1996). “Markov chain Monte Carlo convergence diagnostics: A comparative study,” J. Amer. Statist. Assoc., vol. 91, pp.883–904. 6. Danielsson, J. (1994). Stochastic volatility in asset prices: Estimation with simulated maximum likelihood. Journal of Econometrics 64, 375-400. 7. Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom ination. Econometrica 50, 987-1007. 8. Fridman, M. and L. Harris (1998). A maximum likelihood approach for non-Gaussian stochastic volatility models. Journal of Business and Economic Statistics 16, 284-291. 9. Gallant, A.R., Hsieh, D., Tauchen, G. (1997). Estimation of stochastic volatility models with diagnostics. Journal of Econometrics 81, 1, 159–192. 10. Gelfand, A.E., and Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409. 11. Gelfand, A.E. (1997). Gibbs Sampling, In: Encyclopedia of Statistical Sciences (update), Eds. J. Kotz, C. Read, D. Banks, J. Wiley and Sons, New York, 283-291. 12. Gelman, A. and Rubin, D.B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457-511. 13. Geman, S., and Geman, D. (1984). Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741. 14. Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In Bayesian Statistics 4, eds. J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith. Oxford: Oxford University Press. 15. Geweke, J., (1993). Bayesian treatment of the independent student-t linear model. Journal of Applied Econometrics 8, S19–S40. 16. Geweke, J. (1994). Comment on Bayesian analysis of stochastic volatility. Journal of Business and Economics Statistics 12 (4), 371–417. 17. Geyer, C. J. (1992). Practical Markov chain Monte Carlo. Statistical Science, 7,473--483. 18. Gilks, W. R. (1992). Derivative-free Adaptive Rejection Sampling for Gibbs Sampling. Bayesian Statistics 4, (eds. Bernardo, J., Berger, J., Dawid, A. P., and Smith, A. F. M.)Oxford University Press, 641-649. 19. Gilks, W. R., P. Wild (1993), Adaptive Rejection Sampling for Gibbs Sampling. Applied Statistics, Vol. 41, Issue 2, 337-348. 20. Gilks, W.R., S. Richardson, and D.J. Spiegelhalter (1996). Markov Chain Monte Carlo in Practice. Chapman & Hall, London. 21. Glosten, L., R. Jagannathan, and D. Runkle (1993). On the relation between the Expected value and the volatility of the nominal excess return on stocks. Journal of Finance 48, 1779-1801. 22. Harvey, A. (1990). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, New York. 23. Harvey, A.C., E. Ruiz, and N. Shephard (1994). Multivariate stochastic variance models. Review of Economic Studies 61, 247-264. 24. 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. 25. Heidelberger, P., and P. D. Welch. (1983). Simulation run length control in the presence of an initial transient.Operations Research 31, 6, 1109–1144. 26. Hogg, R. V. and A. T. Craig (1995). Introduction to Mathematical Statistics, 5th edition. Prentice-Hall. 27. Jacquier, E, N.G. Polson, and P.E. Rossi (1994). Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics 12, 371-389. 28. Jacquier, E, N.G. Polson, and P.E. Rossi (2003). Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Working paper. 29. Kim S., Shephard N., and Chib S. (1998). Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361-393. 30. Melino, A. and S.M. Turnbull (1990). Pricing foreign currency options with stochastic volatility.Journal of Econometrics 45, 239-265. 31. Meyer, R., and J.Yu (2000). BUGS for a Bayesian analysis of stochastic volatility models. The Econometrics Journal, 3(2), 198-215. 32. Neal, R. M. (1993). Probabilistic inference using Markov chain Monte Carlo methods. Dept. of Computer Science, University Toronto, 1993. 33. Neal R.M. (1997). Markov chain Monte Carlo methods based on "slicing` the density function. Technical Report No. 9722. Department of Statistics, University of Toronto. 34. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach, Econometrica 59: 347-370. 35. Robert, C. P. and G. Casella (1999). Monte Carlo statistical methods. Springer, New York. 36. Ross, S. M. (2000). Introduction to probability models, 7th ed. Harcourt Academic Press. 37. Shephard, N. and M.K. Pitt (1997). Likelihood analysis of non-Gaussian measurement time series. Biometrika, 84, 653-667. 38. Tauchen, G., Pitts M. (1983). The price variability-volume relationship on speculative markets. Econometrica 51, 485-505. 39. Taylor, S.J. (1982). Financial returns modelled by the product of two stochastic processes | a study of the daily sugar prices 1961-75. In Anderson, O.D., Editor, Time Series Analysis: Theory and Practice, 1, 203-226. North-Holland, Amsterdam. 40. Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion). The Annals of Statistics, 22, 1701--1762. 41. Tsay, R. S. (2002). Analysis of Financial Time Series. A Wiley Interscience Publication. 42. Yu, J., Yang, Z., (2003). A class of nonlinear stochastic volatility models. Working paper. |
| Description | 碩士 國立政治大學 經濟研究所 87258020 91 |
| 資料來源 | http://thesis.lib.nccu.edu.tw/record/#G0087258020 |
| Type | thesis |
| dc.contributor.advisor | 毛維凌 | zh_TW |
| dc.contributor.author (Authors) | 賴耀君 | zh_TW |
| dc.contributor.author (Authors) | Lai,Simon | en_US |
| dc.creator (作者) | 賴耀君 | zh_TW |
| dc.creator (作者) | Lai,Simon | en_US |
| dc.date (日期) | 2002 | en_US |
| dc.date.accessioned | 18-Sep-2009 15:52:30 (UTC+8) | - |
| dc.date.available | 18-Sep-2009 15:52:30 (UTC+8) | - |
| dc.date.issued (上傳時間) | 18-Sep-2009 15:52:30 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0087258020 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/35729 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 經濟研究所 | zh_TW |
| dc.description (描述) | 87258020 | zh_TW |
| dc.description (描述) | 91 | zh_TW |
| dc.description.abstract (摘要) | 針對金融時序資料變異數不齊一的性質，隨機波動模型除了提供於ARCH族外的另一選擇；且由於其設定隱含波動本身亦為一個隨機波動函數，藉由設定隨時間改變且自我相關的條件變異數，使得隨機波動模型較ARCH族來得有彈性且符合實際。傳統上處理隨機波動模型的參數估計往往需要面對到複雜的多維積分，此問題可藉由貝氏分析裡的馬可夫鏈蒙地卡羅法解決。本文主要的探討標的，即在於利用馬可夫鏈蒙地卡羅法估計美元/新台幣匯率隨機波動模型參數。除原始模型之外，模型的擴充分為三部分：其一為隱含波動的二階自我回歸模型；其二則為藉由基本模型的修改，檢測匯率市場上的槓桿效果；最後，我們嘗試藉由加入scale mixture的方式以驗證金融時序資料中常見的厚尾分配。 | zh_TW |
| dc.description.tableofcontents | 一 研究動機與研究目標 二 文獻回顧 2.1 ARCH族模型與隨機波動模型之回顧 2.2貝氏估計與馬可夫鏈蒙地卡羅法 2.2.1 幾個重要的馬可夫鏈相關性質 2.2.2 貝氏估計 2.2.3 馬可夫鏈蒙地卡羅法 2.2.4 Gibbs sampler 2.2.5 Metropolis-Hastings演算法 2.2.6 適應性拒絕抽樣法 2.2.7 馬可夫鏈的疊代次數與抽樣準則 2.2.7.1序列收斂性質的檢定 2.2.7.2抽樣法 2.2.7.3疊代次數的決定依據 三 模型設定與計量方法 3.1 隨機波動模型的設定 3.2 馬可夫鏈蒙地卡羅估計程序 3.2.1參數設定與機率分配假設 3.2.2 Gibbs sampler演算過程 3.3 SV模型之其它衍生模型 3.3.1 Model 2: AR(2)模型 3.3.2 Model 3：槓桿效果的檢定 3.3.3 Model 4：厚尾隨機波動模型 四 實證研究與探討 4.1 資料來源與軟體應用 4.2 馬可夫鏈的模擬程序與抽樣設定 4.3 實證結果與分析 4.3.1 Model 1的實驗結果與分析 4.3.2 Model 2的實驗結果與分析 4.3.3 Model 3的實驗結果與分析 4.3.4 Model 4的實驗結果與分析 五 結論與展望 六 參考文獻 七 附錄 A. Model 1 的程式碼 B. Model 2 的程式碼 C. Model 3 的程式碼 D. Model 4 的程式碼 | zh_TW |
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| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0087258020 | en_US |
| dc.subject (關鍵詞) | 隨機波動模型 | zh_TW |
| dc.subject (關鍵詞) | 馬可夫鏈蒙地卡羅法 | zh_TW |
| dc.subject (關鍵詞) | 貝氏估計 | zh_TW |
| dc.subject (關鍵詞) | 適應性拒絕抽樣法 | zh_TW |
| dc.subject (關鍵詞) | 槓桿效果 | zh_TW |
| dc.subject (關鍵詞) | 厚尾分配 | zh_TW |
| dc.subject (關鍵詞) | Gibbs sampler | en_US |
| dc.subject (關鍵詞) | scale mixture | en_US |
| dc.subject (關鍵詞) | Metropolis-Hastings | en_US |
| dc.subject (關鍵詞) | (c) Geweke convergence diagnostic | en_US |
| dc.title (題名) | 用馬可夫鏈蒙地卡羅法估計隨機波動模型：台灣匯率市場的實證研究 | zh_TW |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | 1. Black, F. (1976). Studies of stock market volatility changes. Proceedings of the American Statistical Association, Business and Economic Statistics Section, 177-181. | zh_TW |
| dc.relation.reference (參考文獻) | 2. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307-327. | zh_TW |
| dc.relation.reference (參考文獻) | 3. Brooks, S. P. (1998). Markov chain Monte Carlo method and its application. The Statistician. 47, 69-100. | zh_TW |
| dc.relation.reference (參考文獻) | 4. Casella, G., George, E.I., (1992). Explaining the Gibbs sampler. The American Statistician 46,167-174. | zh_TW |
| dc.relation.reference (參考文獻) | 5. Cowles, M. and Carlin, B. (1996). “Markov chain Monte Carlo convergence diagnostics: A comparative study,” J. Amer. Statist. Assoc., vol. 91, pp.883–904. | zh_TW |
| dc.relation.reference (參考文獻) | 6. Danielsson, J. (1994). Stochastic volatility in asset prices: Estimation with simulated maximum likelihood. Journal of Econometrics 64, 375-400. | zh_TW |
| dc.relation.reference (參考文獻) | 7. Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom ination. Econometrica 50, 987-1007. | zh_TW |
| dc.relation.reference (參考文獻) | 8. Fridman, M. and L. Harris (1998). A maximum likelihood approach for non-Gaussian stochastic volatility models. Journal of Business and Economic Statistics 16, 284-291. | zh_TW |
| dc.relation.reference (參考文獻) | 9. Gallant, A.R., Hsieh, D., Tauchen, G. (1997). Estimation of stochastic volatility models with diagnostics. Journal of Econometrics 81, 1, 159–192. | zh_TW |
| dc.relation.reference (參考文獻) | 10. Gelfand, A.E., and Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409. | zh_TW |
| dc.relation.reference (參考文獻) | 11. Gelfand, A.E. (1997). Gibbs Sampling, In: Encyclopedia of Statistical Sciences (update), Eds. J. Kotz, C. Read, D. Banks, J. Wiley and Sons, New York, 283-291. | zh_TW |
| dc.relation.reference (參考文獻) | 12. Gelman, A. and Rubin, D.B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457-511. | zh_TW |
| dc.relation.reference (參考文獻) | 13. Geman, S., and Geman, D. (1984). Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741. | zh_TW |
| dc.relation.reference (參考文獻) | 14. Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In Bayesian Statistics 4, eds. J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith. Oxford: Oxford University Press. | zh_TW |
| dc.relation.reference (參考文獻) | 15. Geweke, J., (1993). Bayesian treatment of the independent student-t linear model. Journal of Applied Econometrics 8, S19–S40. | zh_TW |
| dc.relation.reference (參考文獻) | 16. Geweke, J. (1994). Comment on Bayesian analysis of stochastic volatility. Journal of Business and Economics Statistics 12 (4), 371–417. | zh_TW |
| dc.relation.reference (參考文獻) | 17. Geyer, C. J. (1992). Practical Markov chain Monte Carlo. Statistical Science, 7,473--483. | zh_TW |
| dc.relation.reference (參考文獻) | 18. Gilks, W. R. (1992). Derivative-free Adaptive Rejection Sampling for Gibbs Sampling. Bayesian Statistics 4, (eds. Bernardo, J., Berger, J., Dawid, A. P., and Smith, A. F. M.)Oxford University Press, 641-649. | zh_TW |
| dc.relation.reference (參考文獻) | 19. Gilks, W. R., P. Wild (1993), Adaptive Rejection Sampling for Gibbs Sampling. Applied Statistics, Vol. 41, Issue 2, 337-348. | zh_TW |
| dc.relation.reference (參考文獻) | 20. Gilks, W.R., S. Richardson, and D.J. Spiegelhalter (1996). Markov Chain Monte Carlo in Practice. Chapman & Hall, London. | zh_TW |
| dc.relation.reference (參考文獻) | 21. Glosten, L., R. Jagannathan, and D. Runkle (1993). On the relation between the Expected value and the volatility of the nominal excess return on stocks. Journal of Finance 48, 1779-1801. | zh_TW |
| dc.relation.reference (參考文獻) | 22. Harvey, A. (1990). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, New York. | zh_TW |
| dc.relation.reference (參考文獻) | 23. Harvey, A.C., E. Ruiz, and N. Shephard (1994). Multivariate stochastic variance models. Review of Economic Studies 61, 247-264. | zh_TW |
| dc.relation.reference (參考文獻) | 24. 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. | zh_TW |
| dc.relation.reference (參考文獻) | 25. Heidelberger, P., and P. D. Welch. (1983). Simulation run length control in the presence of an initial transient.Operations Research 31, 6, 1109–1144. | zh_TW |
| dc.relation.reference (參考文獻) | 26. Hogg, R. V. and A. T. Craig (1995). Introduction to Mathematical Statistics, 5th edition. Prentice-Hall. | zh_TW |
| dc.relation.reference (參考文獻) | 27. Jacquier, E, N.G. Polson, and P.E. Rossi (1994). Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics 12, 371-389. | zh_TW |
| dc.relation.reference (參考文獻) | 28. Jacquier, E, N.G. Polson, and P.E. Rossi (2003). Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Working paper. | zh_TW |
| dc.relation.reference (參考文獻) | 29. Kim S., Shephard N., and Chib S. (1998). Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361-393. | zh_TW |
| dc.relation.reference (參考文獻) | 30. Melino, A. and S.M. Turnbull (1990). Pricing foreign currency options with stochastic volatility.Journal of Econometrics 45, 239-265. | zh_TW |
| dc.relation.reference (參考文獻) | 31. Meyer, R., and J.Yu (2000). BUGS for a Bayesian analysis of stochastic volatility models. The Econometrics Journal, 3(2), 198-215. | zh_TW |
| dc.relation.reference (參考文獻) | 32. Neal, R. M. (1993). Probabilistic inference using Markov chain Monte Carlo methods. Dept. of Computer Science, University Toronto, 1993. | zh_TW |
| dc.relation.reference (參考文獻) | 33. Neal R.M. (1997). Markov chain Monte Carlo methods based on "slicing` the density function. Technical Report No. 9722. Department of Statistics, University of Toronto. | zh_TW |
| dc.relation.reference (參考文獻) | 34. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach, Econometrica 59: 347-370. | zh_TW |
| dc.relation.reference (參考文獻) | 35. Robert, C. P. and G. Casella (1999). Monte Carlo statistical methods. Springer, New York. | zh_TW |
| dc.relation.reference (參考文獻) | 36. Ross, S. M. (2000). Introduction to probability models, 7th ed. Harcourt Academic Press. | zh_TW |
| dc.relation.reference (參考文獻) | 37. Shephard, N. and M.K. Pitt (1997). Likelihood analysis of non-Gaussian measurement time series. Biometrika, 84, 653-667. | zh_TW |
| dc.relation.reference (參考文獻) | 38. Tauchen, G., Pitts M. (1983). The price variability-volume relationship on speculative markets. Econometrica 51, 485-505. | zh_TW |
| dc.relation.reference (參考文獻) | 39. Taylor, S.J. (1982). Financial returns modelled by the product of two stochastic processes | a study of the daily sugar prices 1961-75. In Anderson, O.D., Editor, Time Series Analysis: Theory and Practice, 1, 203-226. North-Holland, Amsterdam. | zh_TW |
| dc.relation.reference (參考文獻) | 40. Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion). The Annals of Statistics, 22, 1701--1762. | zh_TW |
| dc.relation.reference (參考文獻) | 41. Tsay, R. S. (2002). Analysis of Financial Time Series. A Wiley Interscience Publication. | zh_TW |
| dc.relation.reference (參考文獻) | 42. Yu, J., Yang, Z., (2003). A class of nonlinear stochastic volatility models. Working paper. | zh_TW |