Sequential Bayesian learning in time-varying-parameter (TVP) models

 

Hedibert Freitas Lopes

Professor of Statistics and Econometrics

Head of the Center of Statistics, Data and Decision Sciences

Insper Institute of Education and Research

www.hedibert.org

 

In this 2-hour class we will start reviewing Bayesian sequential learning in linear and Gaussian state-space models and how it is related to the well-known Kalman filter and smoother.  We then show how to perform smoothed Bayesian inference via Markov chain Monte Carlo when either or both linearity and normality are out of the window.  Filtered Bayesian inference is this more general dynamic model framework is facilitated by particle filters.  We illustrate the implementation of all these algorithms by modeling the time-varying variances of Petrobras returns (US market) via stochastic volatility models.

 

1.   GARCH(1,1) versus stochastic volatility AR(1): motivating dynamic modeling (R code)

2.   Modeling COVID-19 death: an exercise in dynamic modeling

3.   Dynamic models (DM)

4.   Sequential Monte Carlo (SMC) methods 

5.   SV-AR(1) for PBR: MCMC, SMC/particle filter and sequential MCMC (data)

 

My textbook and a few review papers

1.     MCMC: Stochastic Simulation for Bayesian Inference, Second Edition, 2006 (with Gamerman)

2.     Dynamic models. In Gelfand, Fuentes, Hoeting and Smith (Eds.), Handbook of Environmental and Ecological Statistics, 2019, 57-80. Chapman & Hall. (with Schmidt)

3.     Dynamic models. In Dey and Rao (Eds.), Handbook of Statistics, Volume 25: Bayesian Thinking, Modeling and Computation, 2005, Chapter 19, 553-588. (with Migon, Gamerman and Ferreira)

4.     Online Bayesian learning in dynamic models: An illustrative introduction to particle methods. In West, Damien, Dellaportas, Polson and Stephens (Eds.), Bayesian Theory and Applications, 2013, 203-228. Clarendon: Oxford University Press. (with Carvalho)

5.     Particle filters and Bayesian inference in financial econometrics, Journal of Forecasting, 2011, 30, 168-209. (with Tsay)

 

My other related papers

  1. Bayesian semi-parametric Markov switching stochastic volatility model, Applied Stochastic Models in Business and Industry, 35, 978-997. (with Virbickaite)
  2. Walk on the wild side: Multiplicative sunspots and temporarily unstable path, American Economic Review, 2019, 109, 1805-1842. (with Ascari and Bonomolo)
  3. Particle learning for Bayesian semi-parametric stochastic volatility model, Econometric Reviews, 2019, 38, 1007-1023. (with Virbickaite, Ausin and Galeano)
  4. On the long run volatility of stocks: time-varying predictive systems, Journal of the American Statistical Association, 2018, 113, 1050-1069. (with Carvalho and McCulloch)
  5. Sequential Bayesian learning for stochastic volatility with variance-gamma jumps in returns (with discussion), Applied Stochastic Models in Business and Industry, 2018, 34, 460-483. (with Warty and Polson).  Discussion by N. Ravishanker + Discussion by R. Soyer + Reply to the discussion.
  6. Efficient Bayesian inference for multivariate factor SV models, Journal of Computational and Graphical Statistics, 2017, 26, 905-917. (with Kastner and Fruehwirth-Schnatter)
  7. Cholesky realized stochastic volatility model, Econometrics and Statistics, 2017, 3, 34-59. (with Shirota, Omori and Piao)
  8. Time-varying extreme pattern with dynamic models, Test, 2016, 26, 131-149. (with Nascimento and Gamerman)
  9. Evaluation and analysis of sequential parameter learning methods in Markov switching stochastic volatility models. In Zeng and Wu (Eds.), State-Space Models and Applications in Economics and Finance, 2013, 23-61. (with Rios)
  10. Sequential parameter learning and filtering in structured AR models, Statistics and Computing, 2013, 23, 43-57. (with Prado)
  11. Analysis of exchange rates via multivariate Bayesian factor stochastic volatility models.  In Lanzarone and Leva (Eds.), The Contribution of Young Researchers to Bayesian Statistics, 2013, 181-186. (with Kastner and Fruhwirth-Schnatter)
  12. Tracking epidemics with Google Flu Trends data and a state-space SEIR model, Journal of the American Statistical Association, 2012, 107, 1410-1426. (with Dukic and Polson)
  13. Particle learning for sequential Bayesian computation (with discussion), Bayesian Statistics 9, 2011, 317-360. (with Carvalho, Johannes and Polson).
  14. Generalized spatial dynamic factor models, Computational Statistics and Data Analysis, 2011, 55, 1319-1330. (with Gamerman and Salazar).
  15. Particle learning and smoothing, Statistical Science, 2010, 25, 88-106. (with Carvalho, Johannes and Polson)
  16. Particle learning for general mixtures, Bayesian Analysis, 2010, 5, 709-740. (with Carvalho, Polson and Taddy).
  17. Time-varying joint distributions through copulas, Computational Statistics and Data Analysis, 2010, 54, 2383-2399. (with Ausin)
  18. Bayesian modeling of financial returns: a relationship between volatility and trading volume, Applied Stochastic Models in Business and Industry, 2010, 26, 172-193. (with Abanto and Migon)
  19. Extracting SP500 and NASDAQ volatility: The credit crisis of 2007-2008, in O’Hagan, A. and West, M. (Eds.), Handbook of Applied Bayesian Analysis, 2010, 319-342. (with Polson)
  20. Bayesian computation in finance, in Chen, M.-H., Dey, D., Mueller, P., Sun, D. and Ye, K. (Eds.)Frontiers of Statistical Decision Making and Bayesian Analysis, 2010, 383-396. (with Hore, Johannes, McCulloch and Polson)
  21. Bayesian inference for stochastic volatility modeling, in Bocker, K. (Ed.) Rethinking Risk Measurement and Reporting: Uncertainty, Bayesian Analysis and Expert Judgement, 2010, 515-551. (with Polson)
  22. Sequential Monte Carlo Estimation of DSGE Models, 2008, Technical Report, University of Chicago Booth School of Business  (with Chen and Petralia)
  23. Spatial dynamic factor models, Bayesian Analysis, 2008, 3, 759-92. (with Salazar and Gamerman)
  24. Factor stochastic volatility with time varying loadings and Markov switching regimes, Journal of Statistical Planning and Inference, 2007, 137, 3082-3091. (with Carvalho)
  25. Time series mean level and stochastic volatility modeling by smooth transition autoregressions: a Bayesian approach, In Fomby (Ed.) Advances in Econometrics: Econometric Analysis of Financial and Economic Time Series/Part B, 2006, Volume 20, 229-242. (with Salazar)
  26. The extended generalized inverse Gaussian distribution for log-linear and stochastic volatility models, Brazilian Journal of Probability and Statistics, 2006, 20, 67-91. (with Silva and Migon)
  27. Spatio-temporal models for mapping the Incidence of malaria in Para, Environmetrics, 2005, 16, 291-304. (with Nobre and Schmidt)
  28. Co-movements and contagion in emergent markets: stock indexes volatilities, In Gatsonis, Kass, Carlin, Carriquiry, Gelman, Verdinelli and West (Eds.), Case Studies in Bayesian Statistics, 2002, Volume VI, 285-300, Springer-Verlag. (with Migon)
  29. Bayesian forecasting and inference in latent structure for the Brazilian industrial production index, Brazilian Review of Econometrics, 2000, 20, 1-26. (with Huerta)
  30. Hyperparameter estimation in forecasting models, Computational statistics and data analysis, 1999, 29, pp. 387-410. (with Moreira and Schmidt)