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Learning Objectives

LEARNING OUTCOMES: Students are expected to gain theoretical knowledge and advanced skills on the econometric analysis of economic phenomena over time.

KNOWLEDGE AND UNDERSTANDING: Students will be able to autonomously develop all the phases of an empirical project aiming at analyzing and forecasting economic time series.

APPLYING KNOWLEDGE AND UNDERSTANDING: Students will be able to understand an apply the main dynamic models that are used in empirical economic analyses.

MAKING JUDGEMENTS: Students will gain the ability to make judgments about implications of the statistical results for the economic issue at hand.

COMMUNICATION SKILLS: Students will be able to present and communicate effectively the results of the empirical analyses on time series data.

LEARNING SKILLS: Students will have the ability to develop and increase their skills through the consultation of the published scientific literature and the use of databases and other information.




This course aims at providing a sound knowledge of the basic statistical tools for modelling economic and financial time series.

Univariate Time Series
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation, Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks, Unit-roots tests, Impulse response function and measures of persistence

Multivariate Time Series
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.

Hamilton, J.D. (1994) "Time Series Analysis", Princeton University Press


The suggested textbookis: Hamilton, J.D. (1994) "Time Series Analysis", Princeton University Press. Further, lecture notes and slides will be distributed and they will consittute the main reference.


Hamilton, J.D. (1994) "Time Series Analysis", Princeton University Press.

Teaching methods

Lesson in class and homework.

Exam Rules

The evalaution consists of a written exam that involves theoretical exercises and questions about the topics of the course. The average mark of the homework (if taken) will be weighted for 20% of the overall mark.
The student should demonstrate to have learned the theory and the advanced skills required for the econometric analysis of empirical phenomenons over time.
Students who withdraw or fail an exam, can re-take the exam in the same session.