Временные ряды и случайные процессы

Бакалавриат 2022/2023

Статус: Курс по выбору (Прикладная математика и информатика)

Направление: 01.03.02. Прикладная математика и информатика

Кто читает: Департамент математики

Где читается: Факультет компьютерных наук

Когда читается: 4-й курс, 3 модуль

Формат изучения: с онлайн-курсом

Онлайн-часы: 20

Охват аудитории: для своего кампуса

Преподаватели: Горяинова Елена Рудольфовна

Язык: английский

Кредиты: 4

Контактные часы: 46

Full 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

Статистическая игра
Студент должен обосновать выбор модели временного ряда, реализация которого будет смоделирована преподавателем.
Индивидуальное домашнее задание
Защита ДЗ по идентификации наблюдаемого временного ряда
контрольная работа
экзамен

Interim Assessment

2022/2023 3rd module
0.4 * экзамен + 0.1 * Статистическая игра + 0.25 * контрольная работа + 0.25 * Индивидуальное домашнее задание

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

Course Syllabus