# Fiches de cours 2016-2017

## Time series

#### Enseignant(s) :

Thibaud Emeric Rolland Georges

English

#### Summary

A first course in statistical time series analysis and applications, including practical work.

#### Content

• Motivation; basic ideas; stochastic processes; stationarity; trend and seasonality.
• Autocorrelation and related functions.
• Stationary linear processes: theory and applications.
• Spectral representation of a stationary process: theory and applications.
• ARIMA, SARIMA models and their use in modelling.
• State-space models: key ideas and applications.
• Prediction of stationary processes.
• Financial time series: stylised facts, volatility, unit roots and non-stationarity, ARCH, GARCH, stochastic volatility and related models.
• Multivariate time series.
• Long memory processes.
• Other topics as time permits.

#### Learning Prerequisites

##### Required courses

Probability and Statistics

##### Recommended courses

Probability and Statistics for mathematicians.  A course in linear models would be valuable but is not an essential prerequisite.

##### Important concepts to start the course

The material from first courses in probability and statistics.

#### Learning Outcomes

By the end of the course, the student must be able to:
• Recognize when a time series model is appropriate to model dependence
• Manipulate basic mathematical objects associated to time series
• Estimate parameters of basic time series models from data
• Critique the fit of a time series model and propose alternatives
• Formulate time series models appropriate for empirical data
• Distinguish a range of time series models and understand their properties
• Analyze empirical data using time series models

#### Teaching methods

Ex cathedra lectures, exercises and computer practicals in the R language in the classroom and at home.

Mini-project based on data chosen by the student.

#### Assessment methods

Mini-project, final exam.

#### Supervision

 Assistants Yes

#### Resources

##### Bibliography

Polycopié is available with slides, problems, bibliography, etc.

##### Notes/Handbook

• Brockwell, P. J. and Davis, R. A. (1996) Introduction to Time Series and Forecasting.
• Springer. Diggle, P. J. (1990) Time Series : A Biostatistical Introduction. Oxford University Press
• Tsay, R. S. (2005) Analysis of Financial Time Series. Second edition. Wiley.
• Shumway, R. H. and Stoffer, D. S. (2011)  Time Series Analysis and its Applications, with R Examples.  Third edition.  Springer-Verlag.

### Semaine de référence

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16 MED 0 1418
16-17  GCB330
17-18
18-19
19-20
20-21
21-22

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand