Master 2019/2020

Time Series Analysis

Type: Elective course (Statistical Learning Theory)

Area of studies: Applied Mathematics and Informatics

Delivered by: Department of Complex System Modelling Technologies

Where: Faculty of Computer Science

When: 1 year, 3 module

Mode of studies: offline

Instructors: Denis Belomestny

Master’s programme: Statistical Learning Theory

Language: English

ECTS credits: 3

Contact hours: 32

Course Syllabus

Abstract

Time Series consist of values of a variable recorded in an order over a period of time. Such data arise in just about every area of science and the humanities, including econometrics and finance, engineering, medicine, genetics, sociology, environmental science. What makes time series data special is the presence of dependence between observations in a series, and the fact that usually only one observation is made at any given point in time. This means that standard statistical methods are not appropriate, and special methods for statistical analysis are needed. This course aims to provide you with a working knowledge of time series analysis methods as applied in economics, engineering and the natural and social sciences. The emphasis is on methods and the analysis of time series data using the R statistical software.

Learning Objectives

• Students will study mathematical foundations of time series analysis and learn how to apply modern methods of time series analysis in practice

Expected Learning Outcomes

• Identify important features on a time series plot
• Identify and interpret an AR(1) model
• Identify a weakly stationary time series
• Identify when and how to take first differences
• Identify and interpret an MA(q) model
• Distinguish MA terms from an ACF
• Distinguish AR terms and MA terms from simultaneously exploring an ACF and PACF
• Recognize and write AR, MA, and ARMA polynomials
• Identify and interpret a non-seasonal ARIMA model
• Distinguish ARIMA terms from simultaneously exploring an ACF and PACF
• Test that all residual autocorrelations are zero
• Convert ARIMA models to infinite order MA models
• Forecast with ARIMA models
• Create and interpret prediction intervals for forecasts
• Identify and interpret additive and multiplicative decompositions
• Decompose a time series.
• Apply a lowess smoother.
• Apply a moving averages smoother.
• Apply a single exponential smoother.
• Create a periodogram in R
• Identify the dominant periods (or frequencies) of a time series
• Model the variance of a time series.
• Identify and interpret ARCH models.
• Simultaneously model multiple variables in terms of past lags of themselves and one anot.
• Model the variance of a time series
• Identify and interpret ARCH models
• Simultaneously model multiple variables in terms of past lags of themselves and one another
• Estimate the spectral density non-parametrically (Daniell kernel & modified Daniell kernel)
• Identify and interpret bandwidth
• Estimate the spectral density parametrically
• Identify and interpret simple fractionally differenced models
• Recognize when to take first differences vs. fractional differences
• Identify and interpret ARFIMA models
• Apply different models within two intervals of a time ser

Course Contents

• Time Series Basics
• MA Models, PACF
• ARIMA models
• Smoothing and Decomposition Methods
• The Periodogram
• VAR(p) Models and ARCH Models
• VAR(p) Models and ARCH Models
• Spectral Analysis
• Fractional Differencing/Threshold Models

Assessment Elements

• Assignments
• Mid-Semester test
• Project
• Final Exam
  Дисциплина не состоялась. Экзамена не будет.

Interim Assessment

• Interim assessment (3 module)
  0.2 * Assignments + 0.4 * Final Exam + 0.2 * Mid-Semester test + 0.2 * Project

Bibliography

Recommended Core Bibliography

• Chatfield, C., & Xing, H. (2019). The Analysis of Time Series : An Introduction with R (Vol. Seventh edition). Boca Raton, Florida: Chapman and Hall/CRC. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2110461
• Time series analysis, Hamilton, J. D., 1994

Recommended Additional Bibliography

• Анализ временных рядов и прогнозирование : учебник для вузов, Афанасьев, В. Н., 2010