Bayesian Analysis

Bayesian Model Selection for Beta Autoregressive Processes

Roberto Casarin, Luciana Dalla Valle, and Fabrizio Leisen

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We deal with Bayesian model selection for beta autoregressive processes. We discuss the choice of parameter and model priors with possible parameter restrictions and suggest a Reversible Jump Markov-Chain Monte Carlo (RJMCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm.

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Bayesian Anal., Volume 7, Number 2 (2012), 385-410.

First available in Project Euclid: 16 June 2012

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Bayesian Inference Beta Autoregressive Processes Reversible Jump MCMC


Casarin, Roberto; Dalla Valle, Luciana; Leisen, Fabrizio. Bayesian Model Selection for Beta Autoregressive Processes. Bayesian Anal. 7 (2012), no. 2, 385--410. doi:10.1214/12-BA713.

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  • Aitchinson, J. (1986). The Statistical Analysis of Compositional Data. London: Chapman & Hall.
  • Albert, J. H. and Chib, S. (1993). “Bayesian analysis of binary and polychotomous response data.” Journal of American Statistical Association, 88: 669–679.
  • Amisano, G. and Casarin, R. (2007). “Particle filters for Markov-Switching Stochastic Correlation Models.” In Proceedings of the Italian Statistical Society Conference, 2007Intermediate Conference, Risk and Prediction, 305–316. CLEUP Padova.
  • Baghestani, H. (2008). “Predicting capacity utilization: Federal Reserve vs time-series models.” Journal of Economics and Finance, 32: 47–57.
  • Bean, C. (1994). “European unemployment: A survey.” Journal of Economic Literature, 32: 573–619.
  • Billio, M. and Casarin, R. (2010). “Identifying Business Cycle Turning Points with Sequential Monte Carlo: An Online and Real-Time Application to the Euro Area.” Journal of Forecasting, 29: 145–167.
  • — (2011). “Beta Autoregressive Transition Markov-switching Models for Business Cycle Analyis.” Studies in Nonlinear Dynamics and Econometrics, 15(4): 1–32.
  • Brooks, S. P., Giudici, P., and Roberts, G. O. (2003). “Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions.” Journal of the Royal Statistical Society, B, 65: 3–55.
  • Datastream (2010). “Datastream International.” Available:
  • Deschamps, P. J. (2008). “Comparing smooth transition and Markov switching autoregressive models of US unemployment.” Journal of Applied Econometrics, 23: 435–462.
  • Ehlers, R. S. and Brooks, S. P. (2008). “Adpative Proposal Construction for Reversible Jump MCMC.” Scandinavian Journal of Statistics, 35: 677–690.
  • Enciso-Mora, V., Neal, P., and Subba Rao, T. (2009). “Efficient order selection algorithms for integer-valued ARMA processes.” Journal of Time Series Analysis, 30: 1–18.
  • Fan, Y. and Sisson, S. (2011). “Reversible Jump Markov chain Monte Carlo.” In S.P. Brooks, G. J., A. Gelman and Meng, X.-L. (eds.), Handbook of Markov Chain Monte Carlo. Chapman & Hall.
  • Ferrari, S. L. P. and Cribari-Neto, F. (2004). “Beta regression for modelling rates and proportions.” Journal of Applied Statistics, 31: 799–815.
  • Green, P. J. (1995). “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination.” Biometrika, 82: 711–732.
  • Grunwald, G. K., Raftery, A. E., and Guttorp, P. (1993). “Time series of continuous proportions.” Journal of the Royal Statistical Society, Series B, 55: 103–116.
  • Klein, L. R. and Su, V. (1979). “Direct estimates of unemployment rate and capacity utilization in macroeconometric models.” International Economic Review, 20: 725–740.
  • Kotz, S. and van Dorp, J. R. (2004). Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications. New Jersey: World Scientific.
  • Lenk, P. J. and DeSarbo, W. S. (2000). “Bayesian Inference for Finite Mixtures of Generalized Linear Models with Random Effects.” Psycometrika, 65: 93–119.
  • McKenzie, E. (1985). “An autoregressive process for beta random variables.” Management Science, 31: 988–997.
  • Nickel, S. A. (1997). “Unemployment and labour market rigidieties: Europe versus North America.” Journal of Economic Perspective, 11: 55–74.
  • Robert, C. P. (2007). The Bayesian Choice, 2nd Edition. New York: Springer Verlag.
  • Robert, C. P. and Casella, G. (2004). Monte Carlo Statistical Methods, 2nd Edition. New York: Springer Verlag.
  • Robert, C. P. and Rousseau, J. (2002). “A Mixture Approach To Bayesian Goodness of Fit.” Technical Report 02009, CEREMADE, University Paris Dauphine.
  • Rocha, V. A. and Cribari-Neto, F. (2009). “Beta autoregressive moving averages models.” Test, 18: 529–545.
  • Rosenthal, J. S. (2011). “Optimal Proposal Distributions and Adaptive MCMC.” In S.P. Brooks, G. J., A. Gelman and Meng, X.-L. (eds.), Handbook of Markov Chain Monte Carlo: Methods and Applications, 93–112. Chapman & Hall.
  • Taddy, M. (2010). “Autoregressive mixture models for dynamic spatial Poisson processes.” Journal of the American Statistical Association, 105: 1403–1427.
  • Vermaak, J., Andrieu, C., Doucet, A., and Godsill, S. J. (2004). “Reversible jump Markov chain Monte Carlo strategies for Bayesian model selection in autoregressive processes.” Journal of Time Series Analysis, 25: 785–809.
  • Wallis, F. K. (1987). “Time series analysis of bounded economic variables.” Journal of Time Series Analysis, 8: 115–123.