Time Series and Stochastic Processes

2023/2024

Учебный год

ENG

Обучение ведется на английском языке

4

Кредиты

Кто читает:

Департамент математики

Статус:

Курс по выбору

Когда читается:

4-й курс, 3 модуль

Преподаватель

Горяинова Елена Рудольфовна

Course Syllabus

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

• In-class assignment
• Проведение идентификации нестационарного временного ряда
  Проведение идентификации реального (или смоделированного преподавателем) нестационарного временного ряда.
• Статистическая игра
• экзамен

Interim Assessment

• 2023/2024 3rd module
  0.25 * In-class assignment + 0.25 * Проведение идентификации нестационарного временного ряда + 0.1 * Статистическая игра + 0.4 * экзамен

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