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## Time Series

• Teacher(s):
• Course given in: English
• ECTS Credits: 3 credits
• Schedule: Spring Semester 2019-2020, 2.0h. course (weekly average)
•  sessions
•  course website
• Related programme: Master of Science (MSc) in Actuarial Science

### Objectives

Important examples of time series data include monthly number of claims filed from an insurance portfolio, cash-flows over time, daily climate data (temperature, snowfall, rainfall), the number of sun spots observed over time etc. Insurance and finance applications aim at explaining the observed time series data in order to understand the underlying phenomenon which can lead to time series models for future predictions. Typically, time series data contain information related to trends, business cycles, sesonality being further subject to residual errors.

This course shall discuss both probabilistic & statistical aspects of stationary time series. Basics of non-stationary & multivariate times series will be also discussed. R will be the main platform for the illustration of various concepts and the statistical analysis of real/simulated time series data.

### Contents

• Introduction to time series data
• ARMA models: basics
• Probabilistic background
• ARMA models revisited
• Non-stationary times series based on ARMA
• Financial time series
• Estimation & prediction
• Multivariate time series

The course will be accompanied by exercises and facultative R programming tasks.

### References

Brockwell, P.J., Davis, R.A. (2002) Introduction to time series and forecasting. Second Edition, Springer
Ruppert, D., Matteson, D.S. (2015) Statistics and data analysis for financial engineering, with R examples. Second Edition, Springer
Shumway, R.H., Stoffer, D.S. (2011) Time series analysis and its applications, with R examples. Third Edition, Springer

### Pre-requisites

Basics in probability

### Evaluation

#### First attempt

Exam:
Written 1h00 hours
Documentation:
Not allowed
Calculator:
Not allowed
Evaluation:

Final online-exam in case of no access to UNIL Campus due to corona-virus

#### Retake

Exam:
Written 1h00 hours
Documentation:
Not allowed
Calculator:
Not allowed
Evaluation:

Retake online-exam in case of no access to UNIL Campus due to corona-virus