## TIME SERIES

## Program

### Updated A.Y. 2018-2019

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

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.

**Textbook:**

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

**Suggested readings:**

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

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