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Delayed startWritten on 11.09.25 (last change on 11.09.25) by Henryk Zähle Due to the lecturer's visiting stay at another university, the in-person sessions of this course will not begin until the third week of lectures, i.e. on October 28. Participants are asked to study Chapter 1 of the lecture slides on their own during the first week of lectures. In the second… Read more Due to the lecturer's visiting stay at another university, the in-person sessions of this course will not begin until the third week of lectures, i.e. on October 28. Participants are asked to study Chapter 1 of the lecture slides on their own during the first week of lectures. In the second week, an exercise sheet focusing on Chapter 1 will be uploaded, which is to be handed in by Tuesday in the third week of lectures. During the lecture slot in the second week (21 October, 8:30-10:00), students will have the opportunity to ask Friedrich Leblang, the course assistant, questions about Chapter 1 and the first exercise sheet. Chapter 1 essentially only provides a rough introduction to the field of time series analysis without a solid mathematical foundation. The central topic of the course — weakly stationary processes — will not be introduced until Chapter 3. Participants are also asked to recall some basic concepts of functional analysis during the second week of lectures: see slides 56–63. |
Lecturer: Prof. Dr. Henryk Zähle.
Assistent: Friedrich Leblang, BSc.
Contents
- foundations of functional analysis
- basic time series model
- weakly stationary time series: basics, spectral theory, filtering
- ARMA models
- statistical inference for weakly stationary time series
- prediction methods for weakly stationary time series
Recommended prerequisites
- Basic courses in Analysis and Linear Algebra (e.g. Analysis I-III, Linear Algebra I-II)
- Stochastics I and II
- Functional Analysis (not necessary, but an advantage)
This course is intended for students of Mathematics or Actuarial and Financial Mathematics or Mathematics & Computer Science.
Participation in the course requires a basic education in mathematics and a sound knowledge in measure-theoretic probability theory (as taught in the courses Stochastics I and II).
Language
The course will be held in English unless all participants speak German.
Lectures
Tuesday, 8:30-10.00, in SR 6 (room 2.17) in building E2 4
Course materials are available here.
Tutorial
Wednesday, 10:15-11:00 (or 12:30-13:15), in SR 1 (room U.37) in building E2 5.
The first tutorial will take place in the fourth week of lectures.
Assignments
There will be weekly assignments, which will be uploaded on Tuesdays. They are available here.
The submission deadline is the following Tuesday at 8:30 am, via CMS.
The solutions will be discussed in the tutorials.
There will be several programming assignments, but these will only be awarded with bonus points.
Exam
At the end of the term, there will be an oral exam.
To be admitted to the exam, you must achieve at least 50% of the total score of the assignments.
Literature
- Kreiß, J.-P. and Neuhaus, G.: Einführung in die Zeitreihenanalyse, Springer
- Brockwell, P.J. and Davis, R.A.: Time Series: Theory and Methods, Springer