An MCMC computational approach for a continuous time state-dependent regime switching diffusion process

References

• G.B. Adesi, H. Rasmussen, and C. Ravanelli, An option pricing formula for the GARCH diffusion model, Comput. Stat. Data Anal. 49 (2005), pp. 287–310. doi: 10.1016/j.csda.2004.05.014
   Web of Science ®Google Scholar
• Y. Ait-Sahalia, Testing continuous-time models of the spot interest rate, Rev. Financ. Stud. 9 (1996), pp. 385–426. doi: 10.1093/rfs/9.2.385
   Web of Science ®Google Scholar
• S. M. Berman, A bivariate Markov process with diffusion and discrete components, Commun. Stat. Stoch. Models 10 (1994), pp. 271–308. doi:10.1080/15326349408807297
   Google Scholar
• P.G. Blackwell, Random diffusion models for animal movement, Ecol. Modell. 100 (1997), pp. 87–102. doi: 10.1016/S0304-3800(97)00153-1
   Web of Science ®Google Scholar
• P.G. Blackwell, Bayesian inference for Markov processes with diffusion and discrete components, Biometrika 90 (2003), pp. 613–627. doi: 10.1093/biomet/90.3.613
   Web of Science ®Google Scholar
• P.G. Blackwell, M. Niu, M.S. Lambert, and S.D. LaPoint, Exact Bayesian inference for animal movement in continuous time, Methods Ecol. Evol. 7 (2016), pp. 184–195. doi:10.1111/2041-210X.12460
   Web of Science ®Google Scholar
• T. Bollerslev, R.Y. Chou, and K.F. Kroner, ARCH modeling in finance: A review of the theory and empirical evidence, J. Econom. 52 (1992), pp. 5–59. doi: 10.1016/0304-4076(92)90064-X
   Web of Science ®Google Scholar
• S. Chib, Calculating posterior distributions and model estimates in Markov mixtures models, J. Econom. 75 (1996), pp. 79–98. doi: 10.1016/0304-4076(95)01770-4
   Web of Science ®Google Scholar
• S. Chib and I. Jeliazkov, Accept–reject Metropolis-Hastings sampling and marginal likelihood estimation, Stat. Neerl. 59 (2005), pp. 30–44. doi: 10.1111/j.1467-9574.2005.00277.x
   Web of Science ®Google Scholar
• S. Chib and N. Shephard, [Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes]: Comment, J. Bus. Econom. Stat. 20 (2002), pp. 325–327.
   Google Scholar
• R.Y. Chou, Volatility persistence and stock valuations: Some empirical evidence using GARCH, J. Appl. Econom. 3 (1988), pp. 279–294. doi: 10.1002/jae.3950030404
   Web of Science ®Google Scholar
• J.E. Dunn and P.S. Gipson, Analysis of radio telemetry data in studies of home range, Biometrics 33 (1977), pp. 85–101. doi: 10.2307/2529305
   Web of Science ®Google Scholar
• G.B. Durham and A.R. Gallant, Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes, J. Bus. Econ. Stat. 20 (2002), pp. 297–338. doi: 10.1198/073500102288618397
   Web of Science ®Google Scholar
• O. Elerian, S. Chib, and N. Shephard, Likelihood inference for discretely observed non-linear diffusion, Econometrica 69 (2001), pp. 959–993. doi: 10.1111/1468-0262.00226
   Web of Science ®Google Scholar
• B. Eraker, MCMC analysis of diffusion models with application to finance, J. Bus. Econ. Stat. 19 (2001), pp. 177–191. doi: 10.1198/073500101316970403
   Web of Science ®Google Scholar
• G.A Fink, Markov Models for Pattern Recognition, Springer-Verlag, Berlin, 2008.
   Google Scholar
• S. Fruhwirth-Schnatter, Finite Mixture and Markov Switching Models, Springer Series in Statistics, New York, NY, 2006.
   Google Scholar
• C. Fuchs, Inference for Diffusion Processes: With Applications in Life Sciences, Springer-Verlag, Berlin, Heidelberg, 2013.
   Google Scholar
• M.K. Ghosh, A. Arapostathis, and S.I. Marcus, Optimal control of switching diffusions with application to flexible manufacturing systems, SIAM J. Control Optim. 31 (1993), pp. 1183–1204. doi: 10.1137/0331056
   Web of Science ®Google Scholar
• A. Golightly and D.J. Wilkinson, Bayesian inference for nonlinear multivariate diffusion models observed with error, Comput. Stat. Data Anal. 52 (2008), pp. 1674–1693. doi: 10.1016/j.csda.2007.05.019
   Web of Science ®Google Scholar
• S. Goutte, A. Ismail, and H. Pham, Regime-switching stochastic volatility model: Estimation and calibration to VIX options, Appl. Math. Finance 24 (2017), pp. 38–75. doi: 10.1080/1350486X.2017.1333015
   Google Scholar
• C. Guihenneuc-Jouyaux, S. Richardson, and I.M. Longini Jr., Modeling markers of disease progression by a hidden Markov process: Application to characterizing CD4 cell decline, Biometrics 56 (2000), pp. 733–741. doi: 10.1111/j.0006-341X.2000.00733.x
   PubMed Web of Science ®Google Scholar
• J. Janczura and R. Weron, Efficient estimation of Markov regime-switching models: An application to electricity spot prices, AStA Adv. Stat. Anal. 96 (2012), pp. 385–407. doi: 10.1007/s10182-011-0181-2
   Web of Science ®Google Scholar
• P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Applications of Mathematics (New York) 23, Springer-Verlag, Berlin, 1992. doi:10.1007/978-3-662-12616-5
   Google Scholar
• J. Krystul and H.A.P. Blom, Monte Carlo simulation of rare events in hybrid systems, Technical Report WP8, Deliverable D8.3. HYBRIDGE, 2004.
   Google Scholar
• X. Li, D. Jiang, and X. Mao, Population dynamical behavior of Lotka–Volterra system under regime switching, J. Comput. Appl. Math. 232 (2009), pp. 427–448. doi: 10.1016/j.cam.2009.06.021
   Web of Science ®Google Scholar
• J. Ma, A Bayesian approach to longitudinal categorical data in a continuous time Markov chain model, Ph.D. thesis, The University of Texas School of Public Health, Houston, TX, 2013.
   Google Scholar
• E.H. Maroufy, E.H. Hibbah, A. Zyad, and T. Ziad, Bayesian estimation of multivariate autoregressive hidden Markov model with application to breast cancer biomarker modeling, in Bayesian Inference. J. T. Prieto, eds., Chapter 7, 2017. doi:10.5772/intechopen.70053
   Google Scholar
• D.B. Nelson, ARCH models as diffusion approximations, J. Econom. 45 (1990), pp. 7–38. doi: 10.1016/0304-4076(90)90092-8
   Web of Science ®Google Scholar
• S. Ogawa, Monte Carlo simulation of non-linear diffusion processes, Jpn. J. Indust. Appl. Math. 9 (1992), pp. 25–33. doi: 10.1007/BF03167193
   Google Scholar
• A. Parton and P.G. Blackwell, Bayesian inference for multistate ‘step and turn’ animal movement in continuous time, J. Agric. Biol. Environ. Stat. 22 (2017), pp. 373–392. doi: 10.1007/s13253-017-0286-5
   Web of Science ®Google Scholar
• V. Rao and Y.W. Teh, Fast MCMC sampling for Markov jump processes and extensions, J. Mach. Learn. Res. 14 (2013), pp. 3295–3320.
   Web of Science ®Google Scholar
• G.O. Roberts and O. Stramer, On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm, Biometrika 88 (2001), pp. 603–621. doi: 10.1093/biomet/88.3.603
   Web of Science ®Google Scholar
• S.B. Shaker, A. Dirksen, P. Lo, L.T. Skovgaard, M. de Bruijne, and J.H. Pedersen, Factors influencing the decline in lung density in a Danish lung cancer screening cohort, Eur. Respir. J. 40 (2012), pp. 1142–1148. doi:10.1183/09031936.00207911
   PubMed Web of Science ®Google Scholar
• I. Siekmann, L.E.I.I. Wagner, D. Yule, C. Fox, D. Bryant, E.J. Crampin, and J. Sneyd, Fast MCMC sampling for Markov jump processes and extensions, Biophys. J. 100 (2011), pp. 1919–1929. doi: 10.1016/j.bpj.2011.02.059
   PubMed Web of Science ®Google Scholar
• G. Sorwar, Estimating single factor jump diffusion interest rate models, Appl. Financ. Econom. 21 (2011), pp. 1679–1689. doi:10.1080/09603107.2011.591729
   Google Scholar
• R.A. Stockley, Biomarkers in chronic obstructive pulmonary disease: Confusing or useful?, Int. J. COPD 4 (2014), pp. 163–177. doi: 10.2147/COPD.S42362
   Google Scholar
• M.A. Tanner and W.H. Wong, The calculation of posterior distributions by data augmentation (with discussion), J. Amer. Statist. Assoc. 82 (1987), pp. 528–540. doi: 10.1080/01621459.1987.10478458
   Web of Science ®Google Scholar
• K. M. C. Tjørve and E. Tjørve, The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family, PLoS ONE 12 (2017), pp. e0178691. doi:10.1371/journal.pone.017869 doi: 10.1371/journal.pone.0178691
   PubMed Web of Science ®Google Scholar
• Y.K. Tse, J. Yu, and X.B. Chang, Estimation of hyperbolic diffusion using MCMC method, in Research Collection, School of Economics, 2002. Available at http://ink.library.smu.edu.sg/soe_research_all/5
   Google Scholar
• E. Tsionas and A. Tassiopoulos, Bayesian implications of ridge regression, Zellner's g-prior, Tech. Rep., Athens University of Economics and Business – Department of Economics, Athens, 2016. Available at SSRN: http://ssrn.com/abstract=238758.
   Google Scholar
• A. van den Hout, J.P. Fox, and R.H. Klein Entink, Bayesian inference for an illness-death model for stroke with cognition as a latent time-dependent risk factor, Stat. Methods Med. Res. 24 (2015), pp. 769–787. doi:10.1177/0962280211426359
   PubMed Web of Science ®Google Scholar
• G. Yin and C. Zhu, Properties of solutions of stochastic differential equations with continuous state-dependent switching, J. Differ. Equ. 249 (2010), pp. 2409–2439. doi: 10.1016/j.jde.2010.08.008
   Web of Science ®Google Scholar
• A.L. Young, N.P. Oxtoby, and S. Ourselin, A simulation system for biomarker evolution in neurodegenerative disease, Med. Image Anal. 26 (2015), pp. 47–56. doi:10.1016/j.media.2015.07.004
   PubMed Web of Science ®Google Scholar