79205 - Longitudinal Data Analysis

Learning outcomes

The course aims to provide students with the methodological foundations of some of the main statistical techniques for analysing data characterised by a particular structure of dependence inherent in observations repeated over time. On the one hand, the course provides students with basic tools for analysing univariate time series, both for forecasting and for interpreting economic and social phenomena. On the other hand, it introduces students to a number of advanced micro-econometric tools, both theoretical and applied, relating to panel data models. By the end of the course, students will be able to apply what they have learnt to real-world cases, having developed an adequate critical understanding regarding the choice of methods and the interpretation of results. Students will also be able to undertake advanced courses in time series and panel data analysis.

Course contents

Time Series Analysis


Intuitive and formal definition of a time series.


Stochastic processes – Definition, characterisation and properties: stationarity, invertibility and ergodicity. Linear processes and Wold’s theorem. Delay operator, difference operator, polynomials in the delay operator. Infinite-order AutoRegressive (AR) and Moving Average (MA) representations of linear stochastic processes. Global and partial autocovariance and autocorrelation functions.


Modelling – Finite-order approximations of infinite-order AR and MA processes: AR(p), MA(q), ARMA(p,q). ARIMA(p,d,q) models for homogeneous non-stationary linear processes. Seasonal ARIMA(p,d,q)(P,D,Q) models for homogeneous non-stationary seasonal linear processes. The Box-Jenkins procedure for the identification, estimation and testing of a seasonal ARIMA model. Analysis of real-world time series.

Analysis of longitudinal data


Introduction to panel data through some examples. Why should we use panel data? Advantages and limitations.


Multilevel models. Introduction. Model specification and estimation. Examples and applications.


Latent curve models. Introduction. Model specification and estimation. Examples and applications.

Readings/Bibliography

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

Theoretical lectures, during which the methodological aspects of the various techniques will be explained, and practical sessions in the laboratory, during which examples of real-world data analysis carried out using various software programmes will be presented and discussed.

Assessment methods

Assessment of learning takes the form of a written examination comprising open-ended questions on all the topics covered during the course for the Time Series Analysis section. These questions consist of open-ended questions on theory, exercises and analysis of real-world data.


As regards the Longitudinal Data Analysis section, the assessment consists of an oral examination involving the discussion of a case study and a review of theoretical content. The assessment will result in a mark which will be averaged with the mark from the first module’s assessment. It is possible to opt out of the mark for this module alone. The examination dates are the same as for Module I (Prof. Bianconcini) and the oral examination will take place immediately after the written examination, so as to allow students who wish to do so to complete the examination in a single day. However, it is possible to sit the two modules in two separate examination sessions, which need not be consecutive.


For the course ‘Longitudinal Data Analysis’, the final mark will be calculated as the average of the marks obtained in the two modules.


Students may reject the final mark for the course a maximum of two times.

Teaching tools

Videoprojection of slides.

Office hours

See the website of Matteo Farnè

See the website of Rossella Miglio