90481 - Advanced Time Series

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.

Readings/Bibliography

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

Further readings will be suggested during the course.

Teaching methods

Recorded lectures, lectures and discussions in class exercises and lab sessions (R, Matlab or Python).

Assessment methods

Either one of the two options will be valid:

1) written exam

2) courseworks and oral discussion.

More details on this follow.

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 homework 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 homework themselves (with the aim of verifying if they have really done and understood the exercises). The final mark will be assigned based on the level of preparation and consciousness of the student. 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.

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