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Course Syllabus

Bachelor 2021/2022

Time Series and Stochastic Processes

Type: Compulsory course
Area of studies: Applied Mathematics and Information Science
Delivered by: Big Data and Information Retrieval School
Where: Faculty of Computer Science
When: 3 year, 1-4 module
Mode of studies: offline
Open to: students of one campus
Instructors: Boris Demeshev, Peter Lukianchenko
Language: English
ECTS credits: 8
Contact hours: 150

Course Syllabus

Full Syllabus

Abstract

This course is conducted at Data Science and Business Analytics program and is provided to 3rd-year undergraduates who have studied a course covering basic probability and statistical inference. A half of this course introduces concepts of Markov chains, random walks, martingales as well as of to the time series. The course requires basic knowledge in probability theory and linear algebra. It introduces students to the modeling, quantification and analysis of uncertainty. The main objective of this course is to develop the skills needed to do empirical research in fields operating with time series data sets. The course aims to provide students with techniques and receipts for estimation and assessment of quality of economic models with time series data. The course will also emphasize recent developments in Time Series Analysis and will present some open questions and areas of ongoing research.
Learning Objectives

Learning Objectives

  • The main objective of this course is to develop the skills needed to do empirical research in fields operating with time-series data sets.
  • The course will emphasize recent developments in Time Series Analysis and will present some open questions and areas of ongoing research.
Expected Learning Outcomes

Expected Learning Outcomes

  • Students get an understanding of techniques and receipts for estimation and assessment of the quality of economic models with time-series data.
Course Contents

Course Contents

  • Discrete-time martingale theory.
  • Continuous-time stochastic processes.
  • Stochastic calculus and differential equations.
  • Continuous-time financial models.
  • Autoregressive-moving average models ARMA (p,q) Moving average models МА(q). Condition of invertibility. Autoregressive models АR(р). Yull-Worker equations. Stationarity conditions. Autoregressive-moving average models ARMA (p,q). Coefficient estimation in ARMA (p,q) processes. Box-Jenkins’ approach Coefficients estimation in autoregressive models. Coefficient estimation in ARMA (p) processes.
  • Forecasting in the framework of Box-Jenkins model. Forecasting, trend and seasonality in Box-Jenkins model.
  • Non-stationary time series, TSP or DSP: methodology of research. Segmented trends and structure changes
  • Regressive dynamic models. Autoregressive models with distributed lags (ADL).
  • Vector autoregression model and co-integration.
  • Time series co-integration. Co-integration regression. Testing of co-integration. Vector autoregression and co-integration. Co-integration and error correction model.
Assessment Elements

Assessment Elements

  • non-blocking FallMock
  • non-blocking Winter Mock
    The exam may be carried out online via distance learning platforms.
  • non-blocking Homework 3-4
  • non-blocking Spring Mock
  • non-blocking Final Exam
    The exam may be carried out online via distance learning platforms.
  • non-blocking UoL Exam
  • non-blocking Quizzes
  • non-blocking Homework 1-2
Interim Assessment

Interim Assessment

  • 2021/2022 2nd module
    0.45 * FallMock + 0.1 * Homework 1-2 + 0.45 * Winter Mock
  • 2021/2022 4th module
    0.65 * UoL Exam + 0.1 * Final Exam + 0.05 * Quizzes + 0.1 * Homework 3-4 + 0.1 * Spring Mock
Bibliography

Bibliography

Recommended Core Bibliography

  • 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
  • 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
  • Mills, T. C., & Markellos, R. N. (2008). The Econometric Modelling of Financial Time Series: Vol. 3rd ed. Cambridge University Press.

Recommended Additional Bibliography

  • Bartoszyński, R., & Niewiadomska-Bugaj, M. (2008). Probability and Statistical Inference (Vol. 2nd ed). Hoboken, N.J.: Wiley-Interscience. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=219782
  • Freund, J. E., Miller, I., & Miller, M. (2014). John E. Freund’s Mathematical Statistics with Applications: Pearson New International Edition (Vol. Eighth edition, Pearson new international edition). Essex, England: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1418305
  • Hogg, R. V., Zimmerman, D. L., & Tanis, E. A. (2015). Probability and Statistical Inference, Global Edition (Vol. Ninth edition. Global edition). Boston: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1419274
  • Larsen, R. J., & Marx, M. L. (2015). An introduction to mathematical statistics and its applications. Slovenia, Europe: Prentice Hall. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.19D77756
  • Lindgren, B. W. (1993). Statistical Theory (Vol. Fourth edition). Boca Raton, Florida: Routledge. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1683924