# I. Course description

The aim of the course is to provide you with the theoretical basis for working with time series models. All concepts are presented in a univariate framework It starts with the simple component model distinguishing between deterministic and random components, and continues with an overview of basic notions of stochastic processes (including limiting results). For the random components, we then introduce linear models for the conditional mean, justify them by means of the Wold decomposition theorem, and discuss the practically extremely relevant case of autoregressive moving average [ARMA] models. Estimation and model selection is discussed in detail for the linear process (especially AR). The course is completed with a brief analysis of selected nonlinear models (including the class of GARCH models for the conditional variance) and nonstationary models.

# II. Contents:

1. Time Series and Stochastic Processes
2. The Components model; Filters
3. Properties of Stochastic Processes
4. The Wold Decomposition; Linear Processes
5. Autoregressive Models
6. Moving Average and ARMA Models
7. Estimation and Forecasting with ARMA Models
8. Nonlinear Models
9. Modelling Conditional Heteroskedasticity
10. Nonstationary Processes; Integration

# III. Prerequisites:

•  Probability theory & inferential statistics (Advanced Statistics I+II or equivalent)

# IV. Method of Assessment:

• Written exam, solving problems similar to those discussed in the tutorial.
• You can earn some bonus points in the computer class.

# VI. Literature:

Some useful introductory textbooks:

• Brockwell, P. J. and R. A. Davis (2002), Introduction to Time Series and Forecasting, 2nd ed., Springer
• Enders, W. (1995, 2003), Applied Econometric Time Series, Wiley
• Lütkepohl, H. and M. Krätzig (2004), Applied Time Series Econometrics, Cambridge University Press
• Hassler, U. (2018), Time Series Analysis with Long Memory in View, Wiley

More rigorous textbooks:

• Brockwell, P. J. and R. A. Davis (1991), Time Series: Theory and methods, 2nd ed., Springer
• Hamilton, J. (1994), Time Series Analysis, Princeton University Press
• Fan, J. and Yao, Q. (2003), Nonlinear Time Series: Nonparametric and parametric methods, Springer

# VI. Schedule:

• course, 2 hrs. per week; there will be new videos each week, and the original time slot is used for live Q&A (BigBlueButton)
• pen&paper tutorial, 2 hrs. every second week (the first one for self-study, then videos)
• non-compulsory computer class: 2 hrs. every second week (videos)
• see univis for exact times of the live sessions!