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# MMath Mathematics and Statistics / Course details

Year of entry: 2021

## Course unit details:Time Series Analysis and Financial Forecasting

Unit code MATH48032 15 Level 4 Semester 2 Department of Mathematics No

### Overview

This course unit covers a variety of concepts and models useful for empirical analysis of time series data.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Probability 1 MATH10141 Pre-Requisite Compulsory
Probability 2 MATH20701 Pre-Requisite Compulsory
Statistical Methods MATH20802 Pre-Requisite Compulsory
Introduction to Statistics MATH10282 Pre-Requisite Compulsory
Regression Analysis MATH38141 Pre-Requisite Compulsory
MATH48032 pre-requisites

Students are not permitted to take more than one of MATH38032 or MATH48032 for credit in the same or different undergraduate year.  Students are not permitted to take MATH48032 and MATH68032 for credit in an undergraduate programme and then a postgraduate programme.

### Aims

To introduce the basic concepts of the analysis of time series in the time domain and to provide the students with experience in analysing time series data.

### Learning outcomes

On successful completion of this course unit students wil be able to:

• Explain the concepts and general properties of stationary and integrated univariate time series.
• Explain the concepts of linear filter and linear prediction, and derive best linear predictors for time series.
• Apply the backwards shift operator and the concept of roots of the characteristic equation to the study of time series models.
• Explain the concepts of autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and seasonal autoregressive integrated moving average (seasonal ARIMA) time series, and derive basic properties thereof.
• Apply the basic methodology of identification, estimation, diagnostic checking and model selection to time series model building.
• Explain some basic concepts in the analysis of multivariate time series - multivariate autoregressive model, joint stationarity and cointegration.
• Explain the concept of heteroscedasticity and derive basic properties of generalised autoregressive conditionally heteroscedastic (GARCH) models.
• Apply principles of statistical inference to evaluate GARCH-like and ARMA-GARCH models fitted to time series, forecast volatility, and infer the presence or absence of properties like leverage and asymmetry in the underlying financial assets.

### Syllabus

• Introduction and examples of economic and financial time series, asset returns. Basic models: white noise, random walk, AR(1), MA(1). [2]
• Stationary time series. Autocovariance and autocorrelation functions. Linear Prediction. Yule-Walker equations. Estimation of autocorrelation and partial autocorrelation functions. [3]
• Models for stationary time series - autoregressive (AR) models, moving average (MA) models, autoregressive moving average (ARMA) models. Seasonal ARMA models. Properties, estimation and model building. Diagnostic checking. [6]
• Non-stationary time series. Non-stationarity in variance - logarithmic and power transformations. Non-stationarity in mean. Determinisitic trends. Integrated time series. ARIMA and seasonal ARIMA models. Modelling seasonality and trend with ARIMA models. [4]
• Filtering, exponential smoothing, seasonal adjustments. [2]
• Multivariate time series. Stationarity, autocorrelation and crosscorrelation. Multivariate autoregressive model. Markov property. Representation of univariate autoregressive models in Markov form. [3]
• Model based forecasting, from ARMA and ARIMA. [3]
• Conditionally heteroskedastic models â€' ARCH-type models. Volatility forecasting. [7]
• Cointegration. [2]
• Examples of non-linear models - threshold AR, bilinear models, regime switching models. [1]

### Teaching and learning methods

Three lectures and one axamples class each week.  In addition students should expect to spend at least six hours each week on private study for this course unit.

### Assessment methods

Method Weight
Other 20%
Written exam 80%
• Coursework: homework assignment weighting 20%.
• End of semester examination: weighting 80%

### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

• (core) Cryer, Jonathan D and Chan, Kung-Sik. Time Series Analysis with Applications in R. Second edition. Springer, 2008.
• (essential) Ruey S. Tsay, Analysis of Financial Time Series, Third Edition , Wiley, 2010.  ISBN: 0-470-41435-9; 13-digits: 978-0470414354
• (recommended) Mills, Terence C. The Econometric Modelling of Financial Time Series. Second edition. Cambridge University Press, 1999.
• (recommended) Cowpertwait, Paul SP and Metcalfe, Andrew V. Introductory Time Series with R. Springer, 2009.
• (further reading) Shumway, Robert H and Stoffer, David S. Time Series Analysis and Its Application: With R Examples. Second edition. Springer, 2006.

### Study hours

Scheduled activity hours
Lectures 24
Tutorials 12
Independent study hours
Independent study 114

### Teaching staff

Staff member Role
Georgi Boshnakov Unit coordinator