28203 - Econometrics (A. C.)

Course Unit Page

Academic Year 2021/2022

Learning outcomes


On successful completion of this course students will be able to:

1. To acquire knowledge of VAR (vector autoregressive) models and associated estimation methods and testing procedures;

2 To learn how to apply VAR modelling to empirical data;

3 To be able to conduct econometric analysis of real data properly and understand the results.


Course contents

Introduction to multivariate time series. Stationarity, ergodicity. Moments. Linear processes. Martingales. Law of Large Numbers and Central Limit Theorems.

Vector Autoregressive (VAR) models for stationary data. Specification and assumptions. Alternative representations of the model. Estimation (OLS, GLS, SUR, MM, ML) and inference. Stationarity conditions. Moving average (MA) representation. Inference on the MA representation. Forecasting.

Introduction to non-stationary time series. Unit roots and permanent shocks. Integrated processes. Unit root tests and stationarity tests: ADF, PP, KPSS. Cointegration and common trends.

Cointegration in VAR models. Error correction mechanism (ECM) representation of the VAR. Cointegration in VAR(1) models and in the general case. Granger representation theorem. Estimation (RRR, ML) of a cointegrated VAR model. Determination of the cointegration rank. Testing hypotheses on the long run equilibrium and on the short run adjustment.

Structural VAR (SVAR) models. Primitive shocks: identification (Choleski). C form of the SVAR. A-B forms. Identification through long run restrictions (Blanchard-Quah) and sign restrictions. Relation with systems of simultaneous equations. Estimation and inference.


Juselius K. (2008) The Cointegrated VAR model. Oxford University Press

Assessment methods


The final exam aims at evaluating the achievement of the following educational targets:

- knowledge of the econometric techniques shown during the frontal lectures

- ability to employ these techniques to analyze and interpret economic phenomena

The exam consists of a written test and an oral test.

In case online exams will be envisaged by the University of Bologna, the structure of the written exam is the same. The exam will be run through Zoom and Exams Online (EOL). Detailed instructions on how to manage and hand in the online exam are available on the course page on the VIRTUALE platform.

The maximum possible score is 30 cum laude, in case all anwers are correct, complete and formally rigorous.

The grade is graduated as follows:

<18 failed
18-23 sufficient
24-27 good
28-30 very good
30 e lode excellent

Teaching tools

Computer lab

Office hours

See the website of Giuseppe Cavaliere

See the website of Emanuele Bacchiocchi