105.695 Introduction to stochastic processes and time series
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2020S, VO, 2.5h, 4.0EC
This course is evaluated following the new mode. Learn more

Course evaluation


  • Semester hours: 2.5
  • Credits: 4.0
  • Type: VO Lecture

Learning outcomes

After successful completion of the course, students are able to

  • manipulate Brownian motions,
  • compute (simple) Ito integrals,
  • compute entrance time, entrance probabilities and other properties of Markov chains,
  • check the stationarity of stochastic processes,
  • compute autocovariance function and other properties of stationary processes,
  • estimate AR processes,
  • compute linear forecasts.

Subject of course

Brownian motion (Wiener process); Definition and properties; construction of the stochastic integral and properties; Ito isometry and Ito formula; Markov chains in discrete time; definition and fundamental formulas; application of the Markov property; classification of states; introduction to time series analysis: stationary processes (in discrete time), auto covariance function, AR processes, ARMA processes, estimation and forecasting.

Teaching methods

Mixed presentations with slides and on blackboard

Mode of examination




Course dates

Mon15:00 - 17:0002.03.2020 - 09.03.2020FH Hörsaal 7 .
Introduction to stochastic processes and time series - Single appointments
Mon02.03.202015:00 - 17:00FH Hörsaal 7 .
Mon09.03.202015:00 - 17:00FH Hörsaal 7 .

Examination modalities

The performance is assessed by an examination at the end of the semester.
See: https://fam.tuwien.ac.at/lehre/pr/


DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Mon11:30 - 13:3028.09.2020FH Hörsaal 1 written09.07.2020 00:00 - 21.09.2020 23:59TISS2020S

Course registration

Begin End Deregistration end
30.01.2020 00:00 27.06.2020 23:59 27.06.2020 23:59



Brzezniak, Zdzislaw; Zastawniak, Tomasz Basic stochastic processes. A course through exercises. Springer Undergraduate Mathematics Series. Springer-Verlag London, Ltd., London, 1999.

Norris, J. R. Markov chains. Reprint of 1997 original. Cambridge Series in Statistical and Probabilistic Mathematics, 2. Cambridge University Press, Cambridge, 1998.

Deistler, Manfred; Scherrer, Wolfgang. Modelle der Zeitreihenanalyse. Mathematik Kompakt,  Birkhäuser, 2018.

Previous knowledge

Basic knowledge of probability theory, random variables, expectation, variance, covariance, ...

Accompanying courses