# 105.695 Introduction to stochastic processes and time series This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2025S 2024S 2023S 2022S 2021S 2020S 2019S 2018S

2023S, VO, 2.5h, 4.0EC

## Properties

• Semester hours: 2.5
• Credits: 4.0
• Type: VO Lecture
• LectureTube course
• Format: Presence

## 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

The course is planned entirely in presence. Changes are possible due to the current COVID situation.

## Course dates

DayTimeDateLocationDescription
Mon16:00 - 18:0006.03.2023 - 24.04.2023FH Hörsaal 3 - MATH VO Einführung in die Stochastischen Prozesse und Zeitreihen
Mon16:00 - 18:0008.05.2023 - 22.05.2023FH Hörsaal 1 - MWB Termin mit Lecture Tube
Mon16:00 - 18:0015.05.2023HS 7 Schütte-Lihotzky - ARCH Termin mit Lecture Tube
Mon16:00 - 18:0005.06.2023HS 18 Czuber - MB Termin mit Lecture Tube
Fri13:00 - 15:0009.06.2023HS 18 Czuber - MB Ersatztermin 1
Mon16:00 - 18:0019.06.2023HS 13 Ernst Melan - RPL Termin mit Lecture Tube
Tue15:00 - 17:0020.06.2023HS 18 Czuber - MB Ersatztermin 2
Fri17:00 - 19:0023.06.2023HS 18 Czuber - MB Prüfungsvorbereitung
Fri16:00 - 18:0022.09.2023FH Hörsaal 4 Prüfungsvorbereitung
Introduction to stochastic processes and time series - Single appointments
DayDateTimeLocationDescription
Mon06.03.202316:00 - 18:00FH Hörsaal 3 - MATH VO Einführung in die Stochastischen Prozesse und Zeitreihen
Mon20.03.202316:00 - 18:00FH Hörsaal 3 - MATH VO Einführung in die Stochastischen Prozesse und Zeitreihen
Mon27.03.202316:00 - 18:00FH Hörsaal 3 - MATH VO Einführung in die Stochastischen Prozesse und Zeitreihen
Mon17.04.202316:00 - 18:00FH Hörsaal 3 - MATH VO Einführung in die Stochastischen Prozesse und Zeitreihen
Mon24.04.202316:00 - 18:00FH Hörsaal 3 - MATH VO Einführung in die Stochastischen Prozesse und Zeitreihen
Mon08.05.202316:00 - 18:00FH Hörsaal 1 - MWB Termin mit Lecture Tube
Mon15.05.202316:00 - 18:00HS 7 Schütte-Lihotzky - ARCH Termin mit Lecture Tube
Mon22.05.202316:00 - 18:00FH Hörsaal 1 - MWB Termin mit Lecture Tube
Mon05.06.202316:00 - 18:00HS 18 Czuber - MB Termin mit Lecture Tube
Fri09.06.202313:00 - 15:00HS 18 Czuber - MB Ersatztermin 1
Mon19.06.202316:00 - 18:00HS 13 Ernst Melan - RPL Termin mit Lecture Tube
Tue20.06.202315:00 - 17:00HS 18 Czuber - MB Ersatztermin 2
Fri23.06.202317:00 - 19:00HS 18 Czuber - MB Prüfungsvorbereitung
Fri22.09.202316:00 - 18:00FH Hörsaal 4 Prüfungsvorbereitung

## 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
Tue12:00 - 14:0017.09.2024FH Hörsaal 1 - MWB written01.01.2024 00:00 - 10.09.2024 23:59TISSPrüfung 2024S (Nebentermin)
Fri13:00 - 15:0021.02.2025FH Hörsaal 1 - MWB written01.01.2025 00:00 - 14.02.2025 23:59TISSPrüfung 2024S (letzter Termin)
Mon11:00 - 13:0030.06.2025FH Hörsaal 1 - MWB written01.04.2025 00:00 - 23.06.2025 23:59TISSPrüfung 2025S
Tue13:00 - 15:0023.09.2025FH Hörsaal 1 - MWB written01.07.2025 00:00 - 16.09.2025 23:59TISSPrüfung 2025S (Nebentermin)

## Course registration

Begin End Deregistration end
31.12.2022 00:00 30.03.2023 23:59 30.03.2023 23:59

## Curricula

Study CodeObligationSemesterPrecon.Info
033 203 Statistics and Mathematics in Economics Mandatory4. Semester
033 205 Financial and Actuarial Mathematics Not specified4. Semester
066 395 Statistics and Mathematics in Economics Mandatory elective

## 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.

## Previous knowledge

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

German