Bayesian Analysis

Comment on Article by Windle and Carvalho

Roberto Casarin

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This article discusses Windle and Carvalho’s (2014) state-space model for observations and latent variables in the space of positive symmetric matrices. The present discussion focuses on the model specification and on the contribution to the positive-value time series literature. I apply the proposed model to financial data with a view to shedding light on some modeling issues.

Article information

Bayesian Anal., Volume 9, Number 4 (2014), 793-804.

First available in Project Euclid: 21 November 2014

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Exponential Smoothing Positive-Valued Processes State-Space Models Stochastic Volatility


Casarin, Roberto. Comment on Article by Windle and Carvalho. Bayesian Anal. 9 (2014), no. 4, 793--804. doi:10.1214/14-BA918.

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  • Carvalho, C. M. and West, M. (2007). “Dynamic Matrix-Variate Graphical Models.” Bayesian Analysis, 2: 69–98.
  • Clark, T. E. (2011). “Real-time density forecasts from Bayesian vector autoregressions with stochastic volatility.” Journal of Business & Economic Statistics, 29(3): 327–341.
  • Fawcett, N., Kapetanios, G., Mitchell, J., and Price, S. (2014). “Generalised density forecast combinations.” Technical report, Bank of England Working Paper 492, Bank of England.
  • Fox, E. B. and West, M. (2011). “Autoregressive models for variance matrices: stationary inverse Wishart processes.” Technical report, ArXiv:
  • Geweke, J. and Amisano, G. (2010). “Comparing and evaluating Bayesian predictive distributions of asset returns.” International Journal of Forecasting, 26: 216–230.
  • — (2011). “Optimal prediction pools.” Journal of Econometrics, 164: 130–141.
  • Grunwald, G. K., Guttorp, P., and Raftery, A. E. (1993). “Prediction rules for exponential family state space models.” Journal of the Royal Statistical Society, Series B, 55: 937–943.
  • Grunwald, G. K., Hamza, K., and Hyndman, R. J. (1997). “Some properties and generalizations of non-negative Bayesian time series models.” Journal of the Royal Statistical Society, Series B, 55: 937–943.
  • Hyndman, R. J., Koehler, A. B., Ord, J., and Snyder, R. D. (2008). Forecasting with exponential smoothing: the state space approach. Springer-Verlag, Berlin.
  • Patton, A. J. and Timmermann, A. (2011). “Forecast Rationality Tests Based on Multi-Horizon Bounds.” Journal of Business & Economic Statistics, 30(1): 1–17.
  • Prado, R. and West, M. (2010). Time Series: Modeling, Computation, and Inference, chapter Multivariate DLMs and Covariance Models, 263–319. Chapman & Hall/CRC.
  • Quintana, J. M. (1985). “A dynamic linear matrix-variate regression model.” Technical report, Research Report 83, Department of Statistics, University of Warwick.
  • Quintana, J. M., Chopra, V. K., and Putnam, B. H. (1995). “Global asset allocation: Stretching returns by shrinking forecasts.” In Proceedings of the ASA Section on Bayesian Statistical Science, 1995 Joint Statistical Meetings, American Statistical Association..
  • Quintana, J. M. and West, M. (1987). “Multivariate time series analysis: new techniques applied to international exchange rate data.” The Statistician, 36: 275–281.
  • Smith, R. L. and Miller, J. E. (1986). “A non-Gaussian state space model and application to prediction of records.” Journal of the Royal Statistical Society, Series B, 48(79-88).
  • Soyer, R. and Tanyeri, K. (2006). “Bayesian portfolio selection with multi-variate random variance models.” European Journal of Operational Research, 171: 977–90.
  • Triantafyllopoulos, K. (2012). “Multi-variate stochastic volatility modelling using Wishart autoregressive processes.” Journal of Time Series Analysis, 33: 48–60.
  • Uhlig, H. (1997). “Bayesian vector autoregressions with stochastic volatility.” Econometrica, 65(1): 59–73.
  • Wang, H. and West, M. (2009). “Bayesian analysis of matrix normal graphical models.” Biometrika, 96(4): 821–834.
  • West, M. and Harrison., J. (1997). Bayesian Forecasting and Dynamic Models. Springer Verlag.
  • Windle, J. and Carvalho, C. (2014). “A tractable state-space model for symmetric positive-definite matrices.” Bayesian Analysis, forthcoming.

See also

  • Related item: Jesse Windle and Carlos M. Carvalho. A Tractable State-Space Model for Symmetric Positive-Deffinite Matrices. Bayesian Anal., Vol. 9, Iss. 4 (2014) 759–792.