This unit should enable the student to acquire the minimal basics for dealing with the study, description, analysis and/or prevision of chronological series with the help of the free software programme, “R”.
In mathematical terms it is a question of understanding the fundamental concepts at stake, in particular the concepts of stationarity and auto-correlation.
The classical probability framework of ARMA models and their extensions (ARIMA, SARIMA) will be presented. The link with regression (case of exogenous predictors) may also be covered.
Finally the case of spatial data will be studied as a natural extension of the previous context. An initiation into geostatistics will be proposed (variography, estimation of variograms and predictors.
| On completion of the unit, the student will be capable of: | Classification level | Priority |
|---|---|---|
| Identifying the different questions linked to temporal and/or spatial datas | 2. Understand | Important |
| Applying a methodology to respond to a given problem | 3. Apply | Important |
| Analysing a simple temporal series with standard tools (ACF and PACF) to construct a probability model | 4. Analyse | Essential |
| Undertaking a global statistics approach, in particular the validation phase | 3. Apply | Important |
| Envisaging the case of spatial or multivariate data | 1. Knowledge | Useful |
| Understanding the concepts of stationarity and autocorrelation within a study | 2. Understand | Important |
| Percentage ratio of individual assessment | Percentage ratio of group assessment | ||||
|---|---|---|---|---|---|
| Written exam: | 50 | % | Project submission: | % | |
| Individual oral exam: | % | Group presentation: | % | ||
| Individual presentation: | % | Group practical exercise: | % | ||
| Individual practical exercise: | % | Group report: | 50 | % | |
| Individual report: | % | ||||
| Other(s): % | |||||
| Type of teaching activity | Content, sequencing and organisation |
|---|---|
| (inter)active Amphitheatre | General presentation with objectives and the issues of temporal series study. First examples and first analyses of an exploratory nature |
| Course | Course on the classical probability approach –stationarisation and stationary models of the ARMA type – numerous illustrations with small examples Alternating with short exercises to become familiar with 2nd order implicit probability calculations (theoretical ACF calculations). |
| Course | Global statistics approach: reference to the common denominator of the major course units, i.e. statistical estimations and practical tests, notably for the validation phase. Numerous exercises to become familiar with the approach |
| Practical courses | Application to a case study using « R » software |
| Course | Experience feedback and provisional results Extensions with exogenous predictors, spatial and multivariate data. Initiation into geostatistics General Conclusion |