90481 - Advanced Time Series

Academic Year 2022/2023

  • Teaching Mode: Blended Learning
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Statistical Sciences (cod. 9222)

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

Prerequisites: linear time series analysis (linear processes, Wold representation, autocovariance and spectral density function, inference on the moments of a linear process) and basic stochastic processes (conditioning, martingales, martingale difference sequences).

Topics covered throughout the course: Time varying parameter models. Parameter driven models: state space models and the Kalman filter. Observation driven models:  GARCH processes and Score driven models. Estimation and inference.

Optional, additional topics: dynamic quantiles, forecast densities, invertibility, long memory processes, 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 Virtuale

Office hours

See the website of Alessandra Luati


Quality education Decent work and economic growth Climate Action Partnerships for the goals

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