Time series modelling

Aims: To introduce important aspects of time series modelling, including model selection, inference, prediction, extensions to non linear models, state space models and beyond.

Learning outcomes: Acquire a theoretical background for modern time series analysis, covering probabilistic structure of time series models, criteria for model selection, parameter estimation, model checking and diagnostics, with practical applications. Be able to describe some of the reasons why linear models may fail to fit real data well, and apply techniques to diagnose such failures. Use some commonly-used extensions, and conduct inference for these models.

Final exam: a single exam, covering all topics, based on the discussion of a paper or an open problem.

Course contents
The course is articulated in three moduli, with final assessment for each of the moduli.

Course contents
The course is articulated in three moduli, with final assessment.

Module 1: Linear state space models (prof. L.Trapin)
- Linear Gaussian models and the Kalman filter
- Maximum likelihood estimation
- Computational aspects

Module 2: Time-varying-parameter models (prof. A.Luati)
- Nonlinear non-Gaussian models
- Maximum likelihood estimation
- Asymptotic theory

Module 3: Nonlinear time series and chaos theory (prof. S.Giannerini)
- Dynamical systems
- Initial value sensitivity in dynamic systems
- Initial value sensitivity in random dynamic systems
- Statistical problems: estimation and testing
- Some examples