# 12511 - Time Series Analysis

• Campus: Bologna
• Corso: First cycle degree programme (L) in Statistical Sciences (cod. 8873)

Also valid for First cycle degree programme (L) in Statistical Sciences (cod. 8873)

## Learning outcomes

The aim of the course is to provide theoretical concepts and methods on time series and panel data analysis such that it is possible to attend advanced time series and microeconometric courses and to perform real data analysis in a critical way.

## Course contents

Time series analysis

Stochastic processes. Definition, characterization (Kolmogorov theorem) and properties: stationarity, invertibilità, ergodicity. Linear processes and Wold theorem. Backshift operator, difference operator and their properties. Polinomyals in the backshift operator. Infinit order AR and MA representations of linear stochastic processes. Global and partial autocovariance and autocorrelation functions.

Modelling. Finite approximation of infinit order AR and infinit order MA processes: AR(p), MA(q), ARMA(p,q) processes. ARIMA(p,d,q) models for nonstationary homogeneus linear processes. SARIMA(p,d,q)(P,D,Q) models for seasonal nonstationary homogeneus linear processes. Box-Jenkins procedure for the identification, estimation, diagnostic of a SARIMA processe. Analysis of real time series.

Panel data analysis

Introduction on panel data through some examples. Why should we use panel data? Benefits and Limitations.

Heteroskedasticity and serial correlation in the error component model.

Latent growth models. Introduction, model specification and estimation. Examples and selected applications.

Bee Dagum E. Analisi delle serie storiche. Modellistica, previsione e scomposizione. Springer-Verlag Italia, Milano, 2001.

Singer J.D. e Willett J.B. Applied longitudinal data analysis: modeling change and event occurrence. Oxford University Press, 2013.

## Teaching methods

Lectures and tutorials are used to help learning the basic statistical notions for times series and panel data analysis. A tutor helps students in pratical exercises and real data applications.

## Assessment methods

The final exam consists on a written test with eight open questions, being six on the time series analysis part and two on panel data analysis. Questions cover all the topics discussed during the course, that is theoretical issues, exercises, and real data analyses.

Slides

## Office hours

See the website of Silvia Bianconcini

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.