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School of Mathematics

# MATH68032 - 2012/2013

General Information
• Title: Time Series Analysis and forecasting in finance
• Unit code: MATH68032
• Credits: 15
• Prerequisites: good background in statistics, particularly hypothesis testing and regression
• Co-requisite units: None
• School responsible: Mathematics
• Members of staff responsible:
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## Specification

### 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.

### Brief Description of the unit

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

### Learning Outcomes

On successful completion of this course unit students will

• have understanding of the basic time series concepts;
• be able to build models to time series data and critically assess them using a variety of methods for exploration of time series data, identification and models selection.

### 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]
• Non-linear models - threshold AR, bilinear models. Cointegration. [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 – ARCH-type models. Volatility forecasting. [7]
• Regime switching models [1].

### Textbooks

• Cryer, Jonathan D and Chan, Kung-Sik. Time Series Analysis with Applications in R.  Second edition. Springer, 2008.
• Mills, Terence C. The Econometric Modelling of Financial Time Series. Second edition. Cambridge University Press, 1999.
• Shumway, Robert H and Stoffer, David S. Time Series Analysis and Its Application: With R Examples. Second edition. Springer, 2006.
• Cowpertwait, Paul SP and Metcalfe, Andrew V. Introductory Time Series with R. Springer, 2009.

### Teaching and learning methods

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

### Assessment

Coursework: homework assignment weighting 20%.
End of semester examination: three hours weighting 80%

## Arrangements

On-line course materials for this course unit.