Modulbeschreibung MA5426

# Modulbeschreibung

## MA5426: Applied Time Series Analysis

### Fakultät für Mathematik

Modulniveau:
Master
Sprache:
Englisch
Semesterdauer:
Einsemestrig
Häufigkeit:
Unregelmäßig
Credits*:
5
Gesamt-
stunden:

150
Eigenstudiums-
stunden:

105
Präsenz-
stunden:

45
* Die Zahl der Credits kann in Einzelfällen studiengangsspezifisch variieren. Es gilt der im Transcript of Records oder Leistungsnachweis ausgewiesene Wert.
Beschreibung der Studien-/Prüfungsleistungen:
In the written exam (60 minutes) with video surveillance, students are asked to solve specific problems in a similar fashion as they have been performed in the homework. They may also be asked to interpret R code and output to suggest and mathematically formulate appropriate time series models for the data at hand. They should be able to use these models to construct and evaluate forecasts. Finally, the students should know about the assumptions made in different models and what their statistical properties are.
Wiederholungsmöglichkeit:
Im Folgesemester: keine Angabe
Am Semesterende: Ja
(Empfohlene) Voraussetzungen:
MA0009 Introduction to Probability and Statistics
recommended: MA4401 Applied Regression, MA3402 Computational Statistics Software knowledge in R
Angestrebte Lernergebnisse:
Upon completion of the module, students
- understand the characteristics of time series data,
- know about time series models in the time and frequency domain,
- are able to derive important properties and know about model assumptions,
- are able to select and fit time series models for data sets using R,- construct and evaluate forecasts.
Inhalt:
Time series models are required when analyzing data collected over time. In this course students will learn about characteristics of time series, such as stationarity, trends and seasonality. The class of ARIMA models will be introduced and their properties, parameter estimation, forecasting and how to select appropriate formulations for data sets will be discussed. After the treatment of these time domain models an introduction will be given to spectral analysis and filtering in the frequency domain to accommodate periodic variations. For modeling financial time series the class of GARCH and stochastic volatility models will be considered. The course finishes with an introduction to linear Gaussian state space models including the Kalman filter. In order to illustrate the application of the different types of time series models, data from different domains will be considered, including environmental science, medicine, biology, finance and economics.
Lehr- und Lernmethode:
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with illustrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. The lectures will be accompanied by practice sessions, in which specific exercises will be solved. These sessions will help students to deepen their understanding of the methods and concepts taught in the lectures and independently assess their progress.
Medienformen:
blackboard and slides
Literatur:
Shumway, Robert H., and David S. Stoffer. Time series analysis and its applications: with R examples. Springer, 2017.
Box, George EP, et al. Time series analysis: forecasting and control. John Wiley & Sons, 2015.
Tsay, Ruey S. An introduction to analysis of financial data with R. John Wiley & Sons, 2014.
Brockwell, Peter J. and Richard A. Davis. Introduction to time series and forecasting. Third Edition. New York: Springer, 2016.
Modulverantwortliche(r):