Time Series Analysis
Content of the Lecture
This course covers the basic facts of time series analysis. Time series analysis is concerned with the description of true data through a stochastic model which is usually assumed to be stationary. The contents of the lecture include:
- Examples of Time Series
- Stationarity of Time Series
- Estimating Trend and Seasonal Components
- Properties of the Autocovariance Function
- Linear filters and Moving Average Processes of Infinite Order
- ARMA Models
- Linear Prediction
- Estimation of the Mean and the Autocovariance
- Estimation for Causal Autoregressive Processes
- A Short Introduction to Spectral Theory
- Wold decomposition (if time permits)
This is a 2+1 lecture (4 Credit Points) that counts towards
- MSc. Finance: Elective course in Financial Mathematics or Stochastic
- MSc. Mathematics/WiMa: Elective course in Financial Mathematics
- Introduction to Measure Theoretic Probability or
- Measure Theory and Stochastics I
Information on Exercise Class and Exam
The exercise class takes places biweekly and will start on Thursday, October 17th.
You can find the exercise sheets on Moodle. The password to sign up for the course will be given to you in the first lecture.
There will be an oral exam of about 20 minutes. The dates and details on how to register will be announced during the lecture.
A list of reference books would cover the following works:
- P. J. Brockwell and R. A. Davis: Time Series: Theory and Methods. 2nd edition, Springer, 1991.
- P. J. Brockwell and R. A. Davis: Introduction to Time Series and Forecasting. 2nd edition, Springer, 2002.
- J.-P. Kreiß and G. Neuhaus: Einführung in die Zeitreihenanalyse. Springer, 2006.
- W. A. Fuller: Introduction to Statistical Time Series. 2nd edition, Springer, 1996.
Additionally, the lecture notes will be available on Moodle.