Prerequisites:
- Basic knowledge of probability theory (more precisely: probability spaces, expectation, variance, covariance, conditional probabilities, Markov's and Hoeffding's inequalities, discrete and continuous real-valued random variables, random vectors, law of large numbers, central limit theorem, multivariate normal distribution).
- Basic knowledge of statistics (more precisely: descriptive statistics, point estimation, linear regression, least squares estimation, ML-estimation, statistical testing, confidence sets).
- Basic knowledge of linear algebra (more precisely: linear equations, matrix algebra, finite dimensional vector spaces, determinants, positive (semi-)definite matrices, eigenvalues and eigenvectors).
- Basic knowledge of calculus (more precisely: limits, (partial) differentiation, integration, calculus of several variables).
Aim of the Course:
For many practical purposes in statistics the assumption that a given set of observations recorded in time has been generated by independent random variables does not serve as an adequate model of reality. Examples are, for instance, the number of an airline's passenger bookings per week, the daily closing values of stock market indices, monthly car accidents, or the yearly beer consumption in a country. Time series analysis accounts for the dependence in observed data that evolves with time.This course is an introduction to the mathematical modeling and statistical analysis of time series.
It starts with the development of the basic concept of stationary stochastic processes, covers the decomposition of time series into trends, seasonalities and residuals, addresses parametric fitting of ARMA models, non-parametric time series analysis, and forecasting procedures. The course content will be accompanied by an introduction to time series analysis by means of the open-source programming language R. In addition to classical topics in time series analysis, popular time series models that have been found to be effective at modeling non-linear behavior of time series data will be introduced.After successfully finishing this course, the students are able to:
-determine descriptive measures of time series.
-decompose time series into systematic and non-systematic components.
-fit linear models to time series data.
+apply techniques for forecasting future values of a time series.
+take non-linear models into account.
+use R functions and packages for analyzing time series data.
Rules about Homework/Exam
The final grade consists of homework (20%) and a written (retake) exam (80%). To pass the course, the grade for the (retake) exam should be at least 5 and the (unrounded) weighted average of the two partial grades at least 5.5. No minimum grade is required for the homework in order to take the exam or to pass the course. The homework counts as a practical and there is no retake for it.
Lecture notes/Literature
Lecture notes can be downloaded. They are based on the course given in 2022 and can change slightly.
For further reading I recommend:
P.J. Brockwell and R.A. Davis: Time Series: Theory and Methods, 2nd edition, 1991
Lecturers
Alexander Dürre
- Docent: Alexander Dürre