Gaetano Carmeci
Università di Trieste
Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche “B. de Finetti” (DEAMS)
Via Tigor 22
34123 Trieste
fax: +39 0405587005;  phone: +39 0405587100


Roberto Casarin, University of Venice, Italy
Matteo Ciccarelli, European Central Bank, DG Economics
Francesco Ravazzolo, Free University of Bozen-Bolzano, Italy


Basic Requirements

Intermediate knowledge of econometrics


The course is advanced and covers state-of-the-art techniques and recent developments in Bayesian Multivariate Models, for structural analysis and forecasting,  nonparametric methods and forecast combinations with a broad range of applications in economics and finance. The methods introduced in the lectures will be illustrated with hands-on applications in MATLAB.


Course outline:

  1. Review of Bayesian estimation
    1. Linear Regression Model (LRM) with spherical and non-spherical errors
    2. LRM with Time varying parameters and stochastic volatility
  2. Multivariate models
    1. Introduction to VAR models
    2. VARs estimated with panel data
    3. Panel VAR models
  3. Bayesian Markov-switching VAR models
    1. Markov-switching (MS) models and Hamilton Filter
    2. MS-VAR and MCMC methods
    3. Multi-country panel MS-VAR
    4. VAR with MS Stochastic Correlation
    5. Application to macroeconomics (e.g. business cycle) and finance (exchange rates and CDS on sovereign bonds)
  1. Structural Graphical VAR Models
    1. Bayesian Networks and MCMC methods for Graphical Models
    2. Graphical VAR models
    3. Applications to macroeconomics and financial contagion
  2. Bayesian Nonparametric Models
    1. Bayesian Nonparametric
      • Dirichlet and Pitman-Yor process priors
      • Infinite mixture representation
      • Dependent Pitman-Yor process priors
      • Slice sampling and MCMC sampling for nonparametric models
    2. Nonparametric VAR models
    3. Nonparametric density combination models
    4. Applications to macroeconomics (business cycle) finance (stock markets).
  3. Forecasting with Bayesian multivariate models
    1. How to compute point and density forecasts from Monte Carlo draws
    2. Evaluation of forecasts
    3. Applications to macroeconomics (GDP growth, inflation, interest rate and unemployment) and finance (electricity prices and cryptocurrencies)
  4. Density forecast combinations
    1. Bayesian model averaging
    2. Extension to time-varying combination weights and learning
    3. Combinations of large data sets
    4. Parallel computation
    5. Applications to macroeconomics and finance


Preliminary readings

  • Handouts, readings and further material will be provided before the beginning of and during the lectures.
  • Ahelegbey D. F., Billio, M. and Casarin, R. (2015), Bayesian Graphical Models for Structural Vector Autoregressive Processes, Journal of Applied Econometrics, forthcoming.
  • Arias, Jonas E. & Rubio-Ramírez, Juan F. & Waggoner, Daniel F., 2014. "Inference Based on SVARs Identified with Sign and Zero Restrictions: Theory and Applications," Dynare Working Papers 30, CEPREMAP.
  • Billio, Casarin, Ravazzolo and van Dijk, 2013. Time-varying Combinations of Predictive Densities using Nonlinear Filtering, Journal of Econometrics, 177(2), 213–232.
  • Canova and Ciccarelli, 2013. Panel Vector Autoregressive Models: A Survey. Advances in Econometrics, eds. T. Fomby, L. Kilian and A. Murphy, Volume 32, 2013.
  • Canova and Ciccarelli, 2012. ClubMed? Cyclical fluctuations in the Mediterranean basin. Journal of International Economics, 88: 162-175.
  • Casarin, R., Sartore, D. and Tronzano, M. (2016), A Bayesian Markov-switching correlation model for contagion analysis on exchange rate markets, Journal of Business and Economic Statistics, forthcoming.
  • Casarin, Grassi, Ravazzolo and van Dijk, 2015. Parallel Sequential Monte Carlo for Efficient Density Combination: The Deco Matlab Toolbox, Journal of Statistical Software, 68(3).
  • Clark and Ravazzolo, 2015. The Macroeconomic Forecasting Performance of Autoregressive Models with Alternative Specifications of Time-Varying Volatility, Journal of Applied Econometrics, 30(4), 551-575.
  • Ciccarelli, Ortega and Valderrama 2015, Heterogeneity and cross-country spillovers in macroeconomic-financial linkages, The B.E. Journal of Macroeconomics, 16: 231-276
  • Ciccarelli, Maddaloni and Peydró, 2015 Trusting the bankers: a new look at the credit channel of monetary policy transmission, Review of Economic Dynamics, 18:979-1002.
  • Del Negro, M. and Schorfheide, F. (2010). Bayesian Macroeconometrics, Handbook of Bayesian Econometrics.
  • Gianfreda, A., F. Ravazzolo and L. Rossini (2018), Comparing the Forecasting Performances of Linear Models for Electricity Prices with High RES Penetration, ArXiv.
  • Lerch, S., T. Thorarinsdottir, F. Ravazzolo and T. Gneiting (2017), Forecaster's Dilemma: Extreme Events and Forecast Evaluation, Statistical Science, 32(1), 106-127.
  • Litterman, R. B. (1986). Forecasting with Bayesian vector autoregressions five years of experience. Journal of Business and Economic Statistics, (4):25-38.
  • Kilian, L. F. (2011). Structural Vector Autoregression, Mimeo.
  • Kim, C.J. and C.R. Nelson (1999), “State-Space Models with Regime Switching,” MIT Press, Cambridge, MA.Koop, G. (2003) Bayesian Econometrics, J. Wiley.
  • West, M., and J. Harrison (1997). Bayesian Forecasting and Dynamic Models, 2nd Ed., Springer, 1997


Participants will use their laptops with MATLAB already installed on them.

Program is conditional to the recruitment of a minimum of 15 participants


Venue : The Module will be held in the Bank of Italy's Scuola di Automazione per Dirigenti Bancari (SADiBa), via San Marco n.54, Perugia. Participants will be accommodated at SADiBa.

Fees and Enrollment

  •  Students, PhD students and temporary university staff: 650€ 
  •  University staff: 800€ 
  •  Others: 2000€

Fee includes: Full board accommodation (usually in double room) starting from Sunday.

Partecipants who wish to attend two or three modules, are allowed the following reduced fees per Module

  •  Students, PhD students and temporary university staff: 550€ per Module
  •  University staff: 700€ per Module
  •  Others: 1600€ per Module