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

Properties

  • 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

Written

Lecturers

Institute

Course dates

DayTimeDateLocationDescription
Mon15:00 - 17:0002.03.2020 - 09.03.2020FH Hörsaal 7 .
Introduction to stochastic processes and time series - Single appointments
DayDateTimeLocationDescription
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/

Exams

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

Curricula

Literature

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

Language

German