Time Series and Stochastic Processes

Bachelor 2025/2026

Type: Elective course (Applied Mathematics and Information Science)

Delivered by: Department of Mathematics

Where: Faculty of Economic Sciences

When: 4 year, 3 module

Open to: students of one campus

Instructors: Elena R. Goryainova

Language: English

ECTS credits: 4

Contact hours: 46

Full Syllabus Ask Question

Abstract

Pre-requisites: basic courses in Calculus, Theory of Probability and Mathematical Statistics.This course presents an introduction to time series analysis and stochastic processes and their applications in operations research and management science. Time series includes the description of the following models: white noise, AR(p), MA(q), ARMA(p,q), ARCH(p), GARCH(p;q) and VAR models. Also, the solution of the problem of identification of the ARMA process, including the model selection, estimation of the model parameters and verification of the adequacy of the selected model, is given. Methods for reducing some non-stationary time series to stationary ones by removing trend and seasonal components are described. Then, the Dolado-Jenkinson-Sosvilla-Rivero procedure is presented to distinguish non-stationary time series such as Trend-stationarity (TSP) and Difference-stationarity (DSP). The procedure for diagnosing the presence of spurious regression is also considered.Stochastic processes are discussed on a basic process Brownian motion and Poisson process. The method for constructing optimal forecasts for Gaussian stochastic processes and stationary time series is given.At the end of the course Markov chains and continuous-time Markov chains are considered. For these models, the conditions for the existence of a stationary distribution are established. In particular, are found the final distribution for the processes of «birth and death» and for the queueing system M/M/n/r.

Learning Objectives

To familiarize students with the concepts, models and statements of the theory of time series analysis and stochastic processes

Expected Learning Outcomes

• Know basics of time series analysis and stochastic processes;
• Be able to choose adequate models in practical socio-economic problems;
Have skills in model construction and solving problems of time series analysis and stochastic processes.

Course Contents

Basic concepts of the theory of stochastic processes
Some types of stochastic processes
Main models of stationary time series
Forecasting
Identification, estimation and testing of ARMA(p,q) models
Identification of nonstationary stochastic processes
Markov chains
Continuous-Time Markov Chains.

Assessment Elements

Проведение идентификации нестационарного временного ряда
Проведение идентификации реального (или смоделированного преподавателем) нестационарного временного ряда.
SG (Participation in the statistical game)
EX (final exam)
Exam form: The exam is conducted in writing using asynchronous proctoring. Asynchronous proctoring means that all the student's actions during the exam will be “watched” by the computer. The exam process is recorded and analyzed by artificial intelligence and a human (Proctor). Please be careful and follow the instructions clearly! Platform for conducting: The exam is conducted on the Moodle platform, an online platform for conducting test tasks of various levels of complexity. Proctoring by using the system Eczemas. The link to the completion of the exam task will be placed in the LMS. You must sign up for the exam 15 minutes before it starts. Technical requirements and rules of the exam: https://elearning.hse.ru/student_steps To participate in the exam, the student must: Prepare an identity document (passport, spread with name and photo) for identification before starting the examination task; Check the operation of the video camera and microphone, the speed of the Internet (for best results, we recommend connecting your computer to the network via a cable); Prepare the tools necessary for completing the examination tasks. Disable applications other than the browser that will be used to log in to the StartExam platform in the computer's task Manager. If one of the necessary conditions for participation in the exam cannot be met, it is necessary to inform the teacher or an employee of the training office about this 7 days before the date of the exam in order to make a decision about the student's participation in the exams. During the exam, students are not allowed to: Turn off the video camera or microphone; Leave the place where the exam task is performed (go beyond the camera's viewing angle); Look away from your computer screen or desktop; Use smart gadgets (smartphone, tablet, etc.); To attract outsiders to assist in the examination, speak with outsiders during the execution of the tasks; Read tasks out loud. Breaking the link: A short-term communication failure during an exam is considered to be the loss of a student's network connection with the Examus platform for no more than 1 minute. A long-term communication failure during an exam is considered to be the loss of a student's network connection to the Examus platform for more than 1 minute. Long-term communication failure during the exam is the basis for the decision to terminate the exam and the rating “unsatisfactory” (0 on a ten-point scale. In case of a long-term violation of communication with the Examus platform during the examination task, the student must notify the teacher, record the fact of loss of communication with the platform (screenshot, response from the Internet provider) and contact the training office with an explanatory note about the incident to make a decision on retaking the exam.
MEX (mid-term exam)

Interim Assessment

2025/2026 3rd module
0.4 * EX (final exam) + 0.2 * MEX (mid-term exam) + 0.1 * SG (Participation in the statistical game) + 0.3 * Проведение идентификации нестационарного временного ряда

Bibliography

Recommended Core Bibliography

Applied econometric time series, Enders, W., 2015
Brockwell, P. J., & Davis, R. A. (2002). Introduction to Time Series and Forecasting (Vol. 2nd ed). New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=108031
Enders, W. (2015). Applied Econometric Time Series (Vol. Fourth edition). Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1639192
Gebhard Kirchgässner, Jürgen Wolters, & Uwe Hassler. (2013). Introduction to Modern Time Series Analysis. Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.spr.sptbec.978.3.642.33436.8
Time series analysis, Hamilton, J. D., 1994
Time series models, Harvey, A. C., 1993
Основы стохастической финансовой математики. Т. 1: Факты. Модели, Ширяев, А. Н., 1998

Recommended Additional Bibliography

Applied econometric time series, Enders, W., 2010
Banerjee, A., Dolado, J. J., Galbraith, J. W., & Hendry, D. (1993). Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data. Oxford University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.oxp.obooks.9780198288107
Box, G. E. P., Reinsel, G. C., & Jenkins, G. M. (2008). Time Series Analysis : Forecasting and Control (Vol. 4th ed). Hoboken, N.J.: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=588017
Dolado, J. J., Jenkinson, T., & Sosvilla-Rivero, S. (1990). Cointegration and Unit Roots. https://doi.org/10.1111/j.1467-6419.1990.tb00088.x
Hamilton, J. D. . (DE-588)122825950, (DE-576)271889950. (1994). Time series analysis / James D. Hamilton. Princeton, NJ: Princeton Univ. Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edswao&AN=edswao.038453134
Harvey, A. C. (1993). Time Series Models (Vol. 2nd ed). Cambridge, Mass: MIT Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=11358
Lütkepohl, H., & Krätzig, M. (2004). Applied Time Series Econometrics. Cambridge, UK: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=164387
Maddala, G. S., & Kim,In-Moo. (1999). Unit Roots, Cointegration, and Structural Change. Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.cup.cbooks.9780521587822
Maronna, R. A. (2018). Robust Statistics : Theory and Methods (with R) (Vol. Second edition). [Place of publication not identified]: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1921437

Authors

GORYAINOVA ELENA RUDOLFOVNA

Course Syllabus