Fundamental knowledge of probability theory, e.g. 'Stochastik 2'. Some basic knowledge in statistics is helpful.

The lecture gives an introduction to time series analysis. Topics that are dealt with:

• Stationary Time Series

* Trend and seasonal components

* Autocorrelation and spectral measure

* ARMA-models

* Wold decomposition

• Statistic in the time domain of stationary processes

* Prediction

* Estimators for mean and autocorrelation function

* Estimation in ARMA models

• Statistic in the frequency domain of stationary processes

* The periodogram

* Nonparametric spectral density estimators

• Extensions and financial time series

* ARIMA and SARIMA models

* GARCH models

If time allows, we will also discuss further topics such as unit-root-tests or multivariate time series.

The material concerning lecture and exercises can be found in the Studierendenportal.

References

• Brockwell, Davis: Time Series: Theory and Methods
• Kreiß, Neuhaus: Einführung in die Zeitreihenanalyse
• Franke, Härdle, Hafner: Statistics of financial markets (dt. Ausgabe: Einführung in die Statistik der Finanzmärkte)