The Italian Econometric Association (SIdE-IEA) in collaboration with the Venice centre in Economic and Risk Analytics for Public Policies (VERA)   organizes the course for PhD students in: 

Advanced Bayesian Econometrics: Bayesian  Multivariate Models and Forecasting in Economics and Finance

29 August – 2 September, 2022
Università Ca' Foscari  Venezia (Italy)



Gaetano Carmeci
Università di Trieste
Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche “B. de Finetti” (DEAMS)
Piazzale Europa, 1
34127 Trieste
tel. +39 0405587100



Roberto Casarin , Ca’ Foscari University of Venice
Matteo Ciccarelli , European Central Bank, DG Economics,  Head of Forecasting and Policy Modelling Division
Carlos Montes-Galdon, European Central Bank, DG Economics, Forecasting and Policy Modelling Division
Francesco Ravazzolo, Free University of Bozen-Bolzano


The maximum number of allowed participants in presence is 20.



Intermediate knowledge of econometrics; intermediate knowledge of Bayesian statistics and MCMC methods.



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

      1.1 Linear Regression Model (LRM) with spherical and non-spherical errors
      1.2 Model comparison and model selection
      1.3 LRM with Time varying parameters and stochastic volatility

2. Multivariate models

      2.1 Introduction to VAR and Panel VAR models
      2.2 VAR with skewed errors

3. Bayesian Markov-switching VAR models

     3.1 Markov-switching (MS) models and Hamilton Filter
     3.2 MS-VAR and MCMC methods 3.3 Multi-country panel MS-VAR
     3.4 VAR with MS Stochastic Correlation
     3.5 Application to macroeconomics (e.g. business cycle) and finance (exchange rates and CDS on sovereign bonds)

4. Structural Graphical VAR Models

      4.1 Bayesian Networks and MCMC methods for Graphical Models
      4.2 Graphical VAR models
      4.3 Applications to macroeconomics and financial contagion

5. Bayesian Nonparametric Models

      5.1 Bayesian Nonparametric

  • Dirichlet and Pitman-Yor process priors
  •  Infinite mixture representation
  •  Dependent Pitman-Yor process priors
  •  Slice sampling and MCMC sampling for nonparametric models

      5.2 Nonparametric VAR models
      5.3 Nonparametric density combination models
      5.4 Applications to macroeconomics (business cycle) and finance (stock markets).

6. Forecasting with Bayesian multivariate models

      6.1 How to compute point and density forecasts from Monte Carlo draws
      6.2 Evaluation of forecasts
      6.3 Applications to macroeconomics and finance

7. Density forecast combinations

      7.1 Bayesian model averaging
      7.2 Extension to time-varying combination weights and learning
      7.3 Combinations of large data sets
      7.4 Parallel computation
      7.5 Applications to macroeconomics and finance

Preliminary readings/Reference textbook for the course

See  the file downloadable  from the public attachment section in this page



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


Venue and timetables

Each Module requires a full-time attendance and participation is not compatible with other jobs at the same time (e.g. preparation of other exams). Lectures and tutorials will be in Englis

  • Monday to Friday: lectures: 9.00/9.30-13.00, 15.00-18.30.

The course will be held in the Campus Economico San Giobbe at Università Ca’ Foscari, Venezia, Italy. Address: Dipartimento di Scienze Economiche - S. Giobbe, 873 - 30121 Venezia.
Participants will be hosted in the Ca' Foscari Residence, inside the Campus Economico San Giobbe (in case of reduced availability of rooms they will be accommodated in local hotels).