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Otoregresif Hareketli Ortalamalar Sürecinde, Tersinir Sıçramalı Markov Zinciri Monte Carlo Yöntemi ile Bayesci Model Seçimi

Year 2007, Volume: 5 Issue: 2, 20 - 29, 14.12.2007

Abstract

Otoregresif hareketli ortalama (ARMA) modellerinde, model derecesinin belirlenmesi için çok değişik yaklaşımlar önerilmiştir. Model derecesinin belirlenmesinde en sık kullanılan Box-Jenkins yönteminde otokorelasyon ve kısmi otokorelasyon katsayılarının grafiklerinden yararlanılır. Bu yöntem deneyime dayalı bir yöntemdir. Otoregresif hareketli ortalama modellerinin derecesinin belirlenmesinde, Bayesci model seçim yöntemleri de kullanılabilir. Tersinir sıçramalı Markov zinciri Monte Carlo (RJMCMC) yöntemi, parametre uzayları arasında sıçramaya olanak tanıyan etkin bir yöntemdir. Bu çalışmada, Troughton tarafından otoregresif süreçler için önerilen tersinir sıçramalı Markov zinciri Monte Carlo algoritması otoregresif hareketli ortalamalar modeline uyarlanmıştır. Önerilen yeni algoritma simülasyon ile üretilen bir zaman serisine uygulanmıştır.

References

  • Box. GEP. and Jenkins G.M .. 1976. Time series analysis. forecasting and control. Holden Day. California.
  • Geweke, J., 1992. EvaIuating the accuracy of sampling-based approaches to the calculation of posterior moments. Bayesian Statistics, 4, J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M Smith, (eds.), pp. 641-649., Oxford: Clarendon Press.
  • Green P. J., 1995. Reversible Jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrica, 82,71 1-732.
  • Monahan J.F., 1983. Fully Bayesian analysis of ARMA time series models. Journal of Econometrics, 21, 307-331.
  • Raftery A.E. and Lewis S.M. 1995. The number of iterations, convergence diagnostics and generic Metropolis algorithms, In Practical Markov Chain Monte Carlo (W.K Gilks, D.J. Spiegelhalter and S. Richardson, eds.), London, Chapman and Hall, 115-130.
  • Troughton P.T. and Godsill J., 1998. A reversible jump sampler for autoregressive time series. Proceddings of IEEE ICASSP-98, IV, 2257-2260.
  • Troughton PT, 1999. Simulation methods for linear and nonlinear time series models with application to distorted audio signals, University of Cambridge, Cambridge.
  • Vermaak J., Andrieu C., Doucet A., Godsill J., 2004. Reversible jump Markov chain Monte Carlo strategies for Bayesian model selection in autoregressive processes. Journal of Time Series Analysis, 25, 785-809.

Bayesian Model Selection with Reversible Jump Markov Chain Monte Carlo Methods in Autoregressive Moving Avarage Processes

Year 2007, Volume: 5 Issue: 2, 20 - 29, 14.12.2007

Abstract

In literature, various approaches have been proposed for determining order of autoregressive moving average models. The most important one is Box-Jenkins aproach. Box-Jenkins method is based on outocorrelations and partial autocorrelations. This method also based on experience. Determining the order of autoregressive moving avarage models Bayesian model selection methods can be used. Reversible jump Markov Chain Monte Carlo method that moves between different model spaces is an influential one. In this study, Troughton's method is modified for determining order of autoregressive moving avarage models. The new method is applied for simulating time series.

References

  • Box. GEP. and Jenkins G.M .. 1976. Time series analysis. forecasting and control. Holden Day. California.
  • Geweke, J., 1992. EvaIuating the accuracy of sampling-based approaches to the calculation of posterior moments. Bayesian Statistics, 4, J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M Smith, (eds.), pp. 641-649., Oxford: Clarendon Press.
  • Green P. J., 1995. Reversible Jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrica, 82,71 1-732.
  • Monahan J.F., 1983. Fully Bayesian analysis of ARMA time series models. Journal of Econometrics, 21, 307-331.
  • Raftery A.E. and Lewis S.M. 1995. The number of iterations, convergence diagnostics and generic Metropolis algorithms, In Practical Markov Chain Monte Carlo (W.K Gilks, D.J. Spiegelhalter and S. Richardson, eds.), London, Chapman and Hall, 115-130.
  • Troughton P.T. and Godsill J., 1998. A reversible jump sampler for autoregressive time series. Proceddings of IEEE ICASSP-98, IV, 2257-2260.
  • Troughton PT, 1999. Simulation methods for linear and nonlinear time series models with application to distorted audio signals, University of Cambridge, Cambridge.
  • Vermaak J., Andrieu C., Doucet A., Godsill J., 2004. Reversible jump Markov chain Monte Carlo strategies for Bayesian model selection in autoregressive processes. Journal of Time Series Analysis, 25, 785-809.
There are 8 citations in total.

Details

Primary Language Turkish
Subjects Statistics
Journal Section Research Articles
Authors

Erol Eğrioğlu

Süleyman Günay This is me

Publication Date December 14, 2007
Published in Issue Year 2007 Volume: 5 Issue: 2

Cite

APA Eğrioğlu, E., & Günay, S. (2007). Otoregresif Hareketli Ortalamalar Sürecinde, Tersinir Sıçramalı Markov Zinciri Monte Carlo Yöntemi ile Bayesci Model Seçimi. İstatistik Araştırma Dergisi, 5(2), 20-29.