Course Unit Page

Academic Year 2020/2021

Learning outcomes

By the end of the course the student is able to analyse data generated by GARCH, DCS, long memory processes and make inference on the moment estimators.

Course contents

Review of linear time series analysis (linear processes, Wold representation, autocovariance and spectral density function, inference on the moments of a linear process).

Advanced time series: non linear processes, observation driven models based on martingale difference sequences.Time varying parameter models: GARCH type processes and Score driven models. Long memory processes.

Advanced frequency domain methods for the spectral analysis of time series. Generalised autocovariances and autocorrelations. Estimation and inference. Introduction to locally stationary processes.


Brockwell P.J. and Davis R.A. (1991), Time series: Theory and Methods, Springer.

Further readings will be suggested during the course.

Teaching methods

Lectures, class exercises and lab sessions.

Assessment methods

Every week during the course, students receive an homework which consists of theoretical questions, exercises and applications to be done with the computer. Students can decide either to do their weekly homeworks and give them to the teacher or to exercise when they like. In the former case, students have direct access to an oral exam which is a discussion of the homweork themselves (with the aim of verifying if they have really done and understood the exercises). In the latter case, students will be required to give a written examination, which essentially is a synthesis of the homework, i.e. it is made by theoretical questions, exercises or proofs and comments to a code. The written exam will be contextually discussed in an oral exam. The final mark will be assigned based on the level of preparation and consciousness of the student.

Teaching tools

Textbook, notes and papers that can be found on the institutional teacher web-site and in IOL

Office hours

See the website of Alessandra Luati