Time series modelling

Proff. Giannerini, Luati, Goracci

  • Date:

    18 APRIL
    22 MAY 2023
  • Event location: Aula IV, Via Belle Arti 41 and STAT PhD Classes Virtual Room

  • Type: Cycle 38 - Mandatory Courses

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.

Module 1: state space models and recent developments (prof. A.Luati)
- Linear Gaussian models and the Kalman filter
- Maximum likelihood estimation
- Non linear non Gaussian models
- Score driven models
- Maximum likelihood estimation
- Illustrations

Module 2: Introduction to nonlinear time series (Prof. G. Goracci)
- Limitation of linear models
- Some parametric nonlinear time series models
- Stationary distributions
- Inference

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