This entry is from Summer semester 2021 and might be obsolete. No current equivalent could be found.

# Time Series Analysis (dt. Zeitreihenanalyse)

 Level, degree of commitment Specialization module, compulsory elective module Forms of teaching and learning,workload Lecture (3 SWS), recitation class (1 SWS) or lecture (2 SWS), recitation class (2 SWS), 180 hours (60 h attendance, 120 h private study) Credit points,formal requirements 6 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics. Duration,frequency One semester, Regularly alternating with other specialization modules Person in charge of the module's outline Prof. Dr. Hajo Holzmann

## Contents

The basic models of time series analysis are discussed with a focus on financial time series, in particular

• Trend and seasonal component, stationarity and autocorrelation
• Autoregression and autoregressive moving average models
• Long-range dependence and unit roots
• Conditional heteroscedasticity and GARCH models
• State space models and the Kalman filter

Data examples and their analysis with R are treated as illustration.

## Qualification Goals

The students shall

• learn the theory and basic models of time series,
• fit them to real data with the help of the statistics software R,
• practice mathematical methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof methods),
• improve their oral communication skills in the recitation classes by practicing free speech in front of an audience and during discussion.

## Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Probability Theory, Internship Stochastics.

## Applicability

The module can be attended at FB12 in study program(s)

• B.Sc. Mathematics
• M.Sc. Data Science
• M.Sc. Computer Science
• M.Sc. Mathematics

When studying M.Sc. Business Mathematics, this module can be attended in the study area Specialization and Practical Modules in Mathematics.

The module can also be used in other study programs (export module).

The module is assigned to Applied Mathematics. Further information on eligibility can be found in the description of the study area.

• Brockwell, P. J. und Davis, R. A. (1991) Time series: theory and methods. 2nd edn. Springer.
• Kreiß, J.-P. und Neuhaus, G. (2006) Einführung in die Zeitreihenanalyse. Springer.
• Tsay, R. S. (2005) Analysis of financial time series. 2nd ed. John Wiley & Sons