MATH-342 / 5 credits

Teacher: Olhede Sofia Charlotta

Language: English

## Summary

A first course in statistical time series analysis and applications.

## Content

• Motivation; basic ideas; stochastic processes; stationarity; trend and seasonality.
• Autocorrelation and related functions.
• Stationary linear processes: theory and applications.
• ARIMA, SARIMA models and their use in modelling.
• Prediction of stationary processes.
• Spectral representation of a stationary process: theory and applications.
• Financial time series: ARCH, GARCH models.
• State-space models:Kalman filter.
• VAR and other simple multivariate time series models
• Other topics as time permits.

## 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

## Teaching methods

Ex cathedra lectures and exercises in the classroom and at home.

## Assessment methods

final exam & mid term assessed coursework - counts for 15%

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

## Supervision

 Assistants Yes Forum No

## Bibliography

Lecturenotes available at https://moodle.epfl.ch/course/view.php?id=15393

## Notes/Handbook

• Brockwell, P. J. and Davis, R. A. (2016) Introduction to Time Series and Forecasting. Third edition. Springer.
• Shumway, R. H. and Stoffer, D. S. (2011) Time Series Analysis and its Applications, with R Examples. Third edition. Springer.
• Tsay, R. S. (2010) Analysis of Financial Time Series. Third edition. Wiley.
• Percival, D.P. and Walden A. T. (1994) Spectral Analysis for Physical Applications. CUP.

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Time series
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Time series
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Time series
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Time series
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Time series
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Time series
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Time series
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Time series
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional

## Related courses

Results from graphsearch.epfl.ch.