The Italian Econometric Society (SIdE) in collaboration with the Venice centre in Economic and Risk Analytics for Public Policies (VERA)  Ca' Foscari University of Venice  organizes the course for PhD students in: 

Bayesian Multivariate Models and Forecasting in Economics and Finance


If the conditions of the ongoing COVID 19 pandemic allow it, the course will  be also delivered in presence. Partecipants may express thier preference upon acceptance

 Venizia (italy) , August 29 - September2, 2022



Gaetano Carmeci
Università di Trieste
Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche “B. de Finetti” (DEAMS)
Via Tigor 22
34124 Trieste
tel. +39 0405587100



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



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  LRM with Time varying parameters and stochastic volatility

  1. Multivariate models

2.1 Introduction to VAR models

2.2 VARs estimated with panel data

2.3 Panel VAR models

  1. 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)

  1. 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

  1. Bayesian Nonparametric Models
    1. 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).

  1. 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 (GDP growth, inflation, interest rate and unemployment) and finance (electricity prices and cryptocurrencies)

  1. 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



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


Preliminary readings/Reference textbook for the course

see the  program outline in the file downloadable  from the public attachment section in this page



Each Module requires 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 English, with the following schedule (provisional):

  • Monday to Friday: lectures: 9.00-13.00, 15.00-17.00 (18.00).


Fees and Enrollment

* Online Course

  • Students, new graduated students, PhD students and temporary university staff: 340 euro 
  • University staff: 450 euro
  • Others: 1500 euro

* Course in Bertinoro

  •  Students, new graduated students, PhD students and temporary university staff: 690€
  •  University staff: 800€ 
  •  Others: 2300€

Fee includes: accommodation breakfast and lunch (starting from Sunday evening).

If participants do not need any accomodation during the course, please send an email to to request a reduced fee and we will apply a cost reduction of 100€.

In case of enrollment in two or more courses, for a maximum of three, Student and Staff participants are entitled to a discount of 100 euros on each course. Other participants are entitled to a discount of 300 euros on each course.


Renounce and refund:

To submit a renounce request, please send an email to

You can give up immediately after the notification of acceptance or later.
After the payment, you can submit your renounce up to one week (7 days) from the beginning of the course (within the terms for refund) and ask for a refund with motivated reasons (health reasons to be documented, for study purposes or personal reasons). We will refund your fee with a deduction for administrative and organization costs: 150 Euro for the course in presence, 100 Euro for online course.
Over the terms for refund (less of 7 days from the beginning of the course) you need to motivate your request (as indicated above), which will be submitted to SIdE President.


Important dates:

Application Deadline: May 10th, 2022

Notification of acceptance will be posted by the 18th May, 2022

Deadline for Fee Payment is June 1th, 2022