- Teacher: Guillaume Mercere
Apprentissage et séries temporelles
In many scientific disciplines, especially in the era of big data, vast amounts of temporal data are available, necessitating advanced analysis tools for tasks such as prediction, diagnostics, decision support, and even simulation. This course on time series analysis aims to provide effective solutions to these classic challenges.
The first part of the course focuses on deterministic methods, covering the following topics:
- Introduction to the "Singular Spectrum Analysis" method for detecting trends and seasonality.
- Modeling trends and seasonality using linear least squares.
- Modeling trends and seasonality using nonlinear least squares.
Building on these tools, the second part of the course delves into the modeling of the random components of data, specifically focusing on:
- Introduction to the concept of time series and stationary stochastic processes.
- Study of the stochastic properties of linear and nonlinear least squares methods.
- Presentation of Wold's theorem for stationary stochastic processes.
- Introduction to AR and ARMA models.
- Overview of least squares solutions for estimating the parameters of AR and ARMA models for stationary time series.
All these concepts will be illustrated through the analysis of time series data available online.