Временные ряды и случайные процессы

Бакалавриат 2022/2023

Лучший по критерию «Новизна полученных знаний»

Статус: Курс обязательный (Прикладной анализ данных)

Направление: 01.03.02. Прикладная математика и информатика

Кто читает: Департамент больших данных и информационного поиска

Где читается: Факультет компьютерных наук

Когда читается: 3-й курс, 1-4 модуль

Формат изучения: с онлайн-курсом

Онлайн-часы: 10

Охват аудитории: для своего кампуса

Преподаватели: Демешев Борис Борисович, Кириллова Мария Андреевна, Лукьянченко Петр Павлович, Попова Светлана Валерьевна

Язык: английский

Кредиты: 8

Контактные часы: 120

Full Syllabus Ask Question

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

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

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

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

Home Assignment 1st module
Fall midterm
Home Assignment 2-4 module
Winter midterm
Spring midterm
Final exam

Interim Assessment

2022/2023 1st module
0.7 * Fall midterm + 0.3 * Home Assignment 1st module
2022/2023 4th module
Module 1 score*0.2+HA (m2-m4)*0.25+Winter Midterm*0.15+Spring Midterm*0.25+Final Exam0.15

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

Authors

Галевская Софья Андреевна
LUKYANCHENKO PETR PAVLOVICH

Course Syllabus