# Time series analysis (FMSN45/MASM17)

## Course contents

Time series analysis concerns the mathematical modeling of time varying phenomena, e.g., ocean waves, water levels in lakes and rivers, demand for electrical power, radar signals, muscular reactions, ECG-signals, or option prices at the stock market. The structure of the model is chosen both with regard to the physical knowledge of the process, as well as using observed data. Central problems are the properties of different models and their prediction ability, estimation of the model parameters, and the model's ability to accurately describe the data. Consideration must be given to both the need for fast calculations and to the presence of measurement errors. The course gives a comprehensive presentation of stochastic models and methods in time series analysis. Time series problems appear in many subjects and knowledge from the course is used in, e.g., automatic control, signal processing, and econometrics.

**Higher education credits**: 7,5 Level: A

**Language of instruction**: The course will be offered in English if non-Swedish speaking students are attending.

**Prerequisites**: Basic courses in probability and statistics, as well as stationary stochastic processes.

**Literature**: Andreas Jakobsson, An Introduction to Time Series Modeling (2nd edition), Studentlitteratur, 2015. The book is also available in an electronic version here.

**Time:** Lectures are held Mondays and Wednesdays 13-15. Exercises are held Thursdays and Fridays; please see the detailed schedule.

**Office hours:** We offer office hours until 20/12. The lecturer will have office hours in MH:217 on Mondays and Wednesdays 11-12. Filip has office hours Tuesdays 9-10. Without appointment, please respect these hours.

## Course material

General material:

- Course program
- Matlab files
- An errata for the textbook is available here.
- Scalable learning videos. Course code: BSNBR-14014.

Lecture notes and schedule:

- Week 1:
- Week 2
- Week 3
- L5: Identification. [slides 1, 2]
- L6: Estimation. [slides 3, 4]
- Reading instructions: Ch. 4, 5.1-5.2
- Textbook problems: 4.1-4.4
- Mini project: [pdf, data]

- Week 4
- L7: Estimation. Model order selection. [slides 1]
- L8: Residual analysis. [slides ]
- Reading instructions: Ch. 5
- Textbook problems: 5.1-5.5, 5.8, 5.10-5.11
- Mini project: [pdf, data]

- Week 5
- L9: Prediction. Multivariate time series. [slides ]
- L10: Multivariate time series. [slides ]
- Reading instructions: Ch. 6, 7
- Textbook problems: 6.1-6.8
- Mini project: [pdf, data]

- Week 6
- L11: Recursive estimation. State space models. [slides ]
- L12: The Kalman filter. Project discussion. [slides ]
- Reading instructions: Ch. 8
- Textbook problems: 7.1-7.4, 8.1-8.2
- Mini project: [pdf, data]

- Week 7
- Textbook problems: 8.3-8.8

## Examination

The course examination consist of mandatory computer exercises, a take-home exam, as well as a project. As a part of the examination, a detailed project report should be handed in, as well as the result being disseminated in an oral presentation (about 10 minutes long).

Course material:

- Computer exercises:
- Exercise 0. [Do this on your own]
- Exercise 1.
- Exercise 2.
- Exercise 3.
- Please be aware that you are expected to come well prepared to the computer exercises. If you have not, you may be asked to leave.

- Project:
- The project will be available here soon. Project examination will take place on
**20/12**, at 10-12, OR on**12/1**, at 13-16. Choose either of these times; you cannot attend without being ready to present. - The project report and the presentation material should be handed in
**no later**than at the start of the presentation. Printed versions of the project report and the take home should be handed in to the course secretary. The slides for the presentation may be mailed as a pdf to the lecturer directly.

- Take home exam:
- The take-home exam will be available here at 12.00 on
**8/1**. The exam is due on**15/1**, at 13.15.

## Advanced courses

After completing this course, you may be interested in the following courses:

- Stationary and non-stationary spectral estimation
- Non-linear time series
- Financial statistics
- Valuation of derivative assets
- We also have several interesting thesis projects.