Scheda insegnamento

Anno Accademico 2018/2019

Conoscenze e abilità da conseguire

At the end of the course the student is able to develop the econometric analysis of the class of present value models used in financial econometrics, using stationary and/or non-stationary Vector Autoregressive systems as statistical platforms upon which all theoretical restrictions are nested and tested.


  1. Introduction.
  2. VAR models: Representation and forecast; Estimation and inference; OLS estimation; ML estimation; Linear constrained estimation; Testing linear restrictions;Tests for Granger causality.
  3. Identification.
  4. Svar: Cholesky, Forecast Error Variance Decomposition, Generalized Impulse Response Analysis
  5. Application on VAR models H-steps variance decomposition matrix: measuring connectedness of financial firms.
Course requirements: background about dynamic econometric models: Basic properties of random sequences; stationary Time Series; The Weak Law of Large Numbers and the Central Limit Theorem; The concepts of DGP and statistical model; Estimation; Hypothesis Testing.


  • Slides provided by the instructor
  • Books:

-Background part (univariate time series):

Hayashi, F. (2000), Econometrics. Princeton University Press (ch 6 and 11)

-Multivariate time series:

Lütkepohl, H. (2006), "New Introduction to multiple Time Series Analysis" , Springer, edizione 2006 - ISBN 978-3-540-262398 (ch. 2.1 all, 2.21 and 2.2.2, 2.3. 3.1, 3.2 and 3.4. 3.6.1 and 3.6.2. 9.1 and 9.4)

  • Papers:

-Diebold, F. X., & Yılmaz, K. (2014). On the network topology of variance decompositions: Measuring the connectedness of financial firms. Journal of Econometrics, 182(1), 119-134.

-Sander, H., & Kleimeier, S. (2003). Contagion and causality: an empirical investigation of four Asian crisis episodes. Journal of International Financial Markets, Institutions and Money, 13(2), 171-186.

  • Suggested:

-Billio, M., Getmansky, M., Lo, A. W., & Pelizzon, L. (2012). Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics, 104(3), 535-559.

-Hamilton, J.D. (1994), Time Series Analysis, Princeton University Press. (Ch. 11)

-Verbeek, M. (2000), A guide to modern econometrics. Wiley (introductory).

-Verbeek (2006) Econometria [testo tradotto in italiano, a cura di S. Pastorello].

-Cappuccio, N., & Orsi, R. (2011), Introduzione all'Econometria, Giappichelli Editore (intermediate).



Metodi didattici

Classes, labs with empirical applications and discussions, and exercises.


Modalità di verifica dell'apprendimento

The exam is written and it lasts 1 hour. It is composed by two different sections.

The first section is theoretical, and it consists of 2 open questions. The second is both empirical and theoretical, and it consists of 5 questions whose answers should be computed using Matlab. Each answer is valid 5 points max; The final mark is the total number of point obtained in the two parts. Students with final number of points greater or equal 33 qualify for getting the mark 30 cum laude.

Strumenti a supporto della didattica


-software: matlab

-matlab toolbox provided by Ambrogio Cesa Bianchi and slides of Identification examples.

-matlab toolbox provided by Ken Nyholm to implement spillover analysis using variance-decomposition, i.e. Diebold-Yilmaz approach.

-data: Oxford Man Realized Volatility dataset (provided by the instructor)

-e-learning platform

Orario di ricevimento

Consulta il sito web di Tiziano Arduini