## TIME SERIES

## Syllabus

EN
IT

### Learning Objectives

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

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

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

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

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

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

### Prerequisites

Mathematics

Statistics

Linear regression model

Statistics

Linear regression model

### Program

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

Forecasting

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.

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

Forecasting

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.

### Books

Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley.

### Bibliography

Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .

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

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

### Teaching methods

Lesson and practice in class, homework.

### Exam Rules

The evaluation 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.

The exam cannot be taken twice in the winter session.

The student should demonstrate to have learned the theory and the advanced skills required for the econometric analysis of empirical phenomenons over time.

The exam cannot be taken twice in the winter session.