Model Volatilitas Stokastik dengan Metode Markov Chain Monte Carlo

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Alfian Alfian

Abstract

Salah satu pendekatan alternatif untuk menjelaskan perubahan volatilitas dalam runtun waktu finansial adalah model volatilitas stokastik. Dalam estimasi model volatilitas stokastik, bentuk eksplisit sangat susah ditentukan sehingga fungsi likelihood distribusi return  ditentukan secara implisit menggunakan variabel bantu atau laten yang melakukan parameterisasi varians yang bersifat stokastik. Untuk itu, metode Bayesian diperlukan dalam estimasi parameter model. Pada tulisan ini difokuskan pada  estimasi Bayesian dengan Metode  Markov Chain Monte Carlo (MCMC).

An alternative approach to describe the volatility changes of a financial time series is stochastic volatility model. In the estimation of stochastic volatility models, an explicit form is very difficult to be determined so that the likelihood function of the return distribution implicitly defined using auxiliary variables or latent stochastic that parameterize the stochastic variance terms.  For that reason, Bayesian methods are needed in the estimation of model parameters. In this thesis focuses on Bayesian estimation with using Markov Chain Monte Carlo Methods (MCMC). 

Article Details

Section
Statistics

References

[1] Albert, J., Bayesian Computation with R, Springer, New York, 2007

[2] Bain, L. J and Engelhardt, M., Introduction to Probability and Mathematical Statistic, Duxbury Press, California, 1992

[3] Bartle, R. G., Sherbert, D. R., Introduction to Real Analysis,3rd edition, John Wiley and Sons, New York, 2000

[4] Bernardo, J.M., Smith, A.F.M., Bayesian Theory, John Wiley and Sons, New York, 1994

[5] Bierens, Herman J., Introduction To The Mathematical and Statistical Foundations Of Econometrics, Cambridge University Press, New York, 2005

[6] Billingsley, P., Convergence of Probability Measures. John Wiley & Sons, New York, 1968

[7] Clark, P. K., A Subordinated Stochastic Process Model With Fixed Variance For Speculative Prices, Econometrica, 1973

[8] Geman, S., and Geman, D., Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, pp.721-741, 1984

[9] Geyer, C.J., Practical Markov Chain Monte Carlo, The Statistical Science, Vol. 7, pp. 473-511, 1992

[10] Gilks, W.R., Wild, P., Adaptive rejection sampling for Gibbs sampling. Applied Statistics, Vol. 41, pp. 337-348, 1992

[11] Jacquier, E., Polson, N. G., and Rossi, P. E., Bayesian analysis of stochastic volatility models (with discussion). Journal of Business & Economic Statistics 12: pp. 371417, 1994

[12] Kim, S., Shephard, N., and Chib, S., Stochastic Volatility: Likelihood inference and comparison with ARCH models, Review of Economic Studies, Vol. 65, pp. 361-393, 1998

[13] Meyer, R. and Yu J., BUGS for a Bayesian analysis of stochastic volatility models. Econometrics Journal 3, pp. 198215, 2000

[14] Rausand, M., Hoyland, A., System Rebility Theory, 2ndedition. Springer Verlag, Berlin, 2004

[15] Ross, Sheldon M., Stochastic processes 2nd edition, John Wiley & Sons, Canada, 1996

[16] SAS Development Core Team, SAS/STAT®9.2 Users Guide, Second Edition, SAS Institute Inc., Cary, NC, USA, 2009

[17] Serfozo, R, Basics of Applied Stochastic Processes, Springer-Verlag, Berlin Heidelberg, 2009

[18] Soejoeti Z, Subanar, Inferensi Bayesian, Penerbit Karunia Universitas Terbuka, Jakarta, 1988

[19] Shephard, N., Fitting non-linear time series models, with applications to stochastic variance models, Journal of Applied Econometrics, Vol. 8, pp. 135-152., 1993

[20] Shephard, N., Statistical aspects of ARCH and stochastic volatility, Time Series Models In econometrics, finance, and other fields.Chapman and Hall, Chapter 1, pp. 1-55, 1996

[21] Shephard N., Stochastic Volatility (Selected Readings). Oxford University Press Inc., New York, 2005

[22] Tsay, R. S., Analysis of Financial time Series 2nd edition. John Wiley and Son, Inc., Hoboken, New Jersey, 2005

[23] Wantanee, S., Bayesian Markov chain Monte Carlo (MCMC) For stochasticVolatilityModelUsingFXDatahttp://69.175.2.130/~finman/Barcelona/Papers/WS_FMAspain07.pdf, 2007

[24] Wei, W. S., Time Series Analysis: Univariate and Multivariate Methods. Addison Wesley, 1994