The course provides a (medium-level) introduction into major aspects of time series analysis, both conceptually (theoretically) and by means of complementing practical applications in the exercises. Students are able to specify adequate models for stationary and integrated time series, and use the estimated models for analysis, including forecasting, but also structural analysis. Students are also aware of potential pitfalls and problems. The outline is to a certain extent tentative and can and will be adjusted to the pre-knowledge and interests of the students.

The course combines lectures and practice sessions, with the practice sessions consisting of discussions of both "pencil and paper" as well as computer exercises using both simulated and real-world data. Many software packages and/or programming languages/environments are being used in time series analysis. In the practice sessions, the software used will be R (potentially also MATLAB or Python).

Encompassing ListIntroductionDescriptive Time Series AnalysisNaive Forecasting MethodsHilbert Spaces (*)Stationary ProcessesSpectral Analysis (*)Parameter Estimation for Stationary and Causal VAR ProcessesRegression with Integrated ProcessesVAR Cointegration AnalysisStructural VAR ModelsThe item list is encompassing – and in this form too much for our allocated time, therefore we will make a “sensible” selection, based on:Prior knowledgeSpecific interests (compatible with prior knowledge)Some of the slide decks are voluminous and contain a lot of material that will not all be covered, but may serve as a source of future reference.The mathematics/statistics of TSE tends to become relatively involved relatively quickly and thus proofs will be TSE II designated.

Understanding of basic mathematical statistics and some linear algebra is most useful for successful participation in the course. Some familiarity with real analysis and stochastic processes would facilitate the understanding of technical details but is not required. To some extent and within bounds, the course can be, as mentioned, adapted to the prior knowledge of the participants. The most important ingredients are motivation and willingness to learn about time series methods.

Curriculum MEDS 23W:CBK1 and CBK2

Teaching MaterialsDuring the semester slides, background material – and of course the exercise sheets and data for the practice sessions – will be uploaded to the Moodle course.The slides do not contain proofs of mathematical results – these will be developed in the classroom on the blackboard.The course does not follow a specific textbook closely.There is a large number of good – partly specific, partly general – time series books, some are listed in the Moodle course; note that they differ substantially in content and complexity.SoftwareThere is no unique market leader when it comes to software used for time series analysis.There are programming languages or environments like:MATLAB, GAUSSPythonRThere are also (more or less) user-friendly and powerful (“clickable”) software environments like:EViewsStatagretlJMulti: closed-shop

Examination MethodologyContinuous assessment of the practice sessions:Tick the exercises you have solved and upload the solutions until Wednesday noon (12pm) prior to the practice session in which the corresponding exercise sheet is discussed.During the exercise sessions you will be randomly selected to present your (uploaded) solutions (to ticked exercises).You are expected to give a short and succinct presentation of your solutions.If it turns out that you are absent (without excuse) or have not prepared the exercise, you will be penalized with up to 5 minus points. In addition, you will lose the point for the exercise you ticked in the list (or all if you are absent).Serious flaws in the solutions presented will lead to deductions.You may, however, also be awarded bonus points for particulary good explanations of exercises and contributions (to the discussions).In order to be eligible for the two-part final exam you have to tick at least 50% of the exercises during the semester (related to TSE I only or TSE I & TSE II).The practice sessions will contribute 50% to the overall grade.Two-part final exam:Preparation of a small report (a few pages only).Oral exam: Covering all topics discussed during the semester in the lectures and practice session as well as the small report (related to TSE I only or TSE I & II). Individual dates to be agreed upon.The two-part final exam will contribute 50% to the overall grade.

All topics covered in the lectures and practice sessions (differentiated into TSE I only or TSE I & II), unless clearly otherwise stated in the lectures.

Exercises, report, oral exam.