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School of Mathematics

# MATH48032 - 2011/2012

General Information
• Title: Time Series Analysis
• Unit code: MATH48032
• Credits: 10
• This course unit cannot be taken as well as MATH38032 which is a level 3 version of the same course unit.
• Prerequisites: MATH20701, MATH20802
• 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

Time series analysis deals with data collected over time. Such data are very common in society, science, engineering, finance, and may represent, for example, daily temperatures, daily stock prices, quarterly economic indicators, monthly house prices. The purpose of the analysis of a time series may be to predict future values, to discover trends and periodicities, or to better understand the underlying process for decision purposes. We introduce basic techniques, methods and models that may be used to this end.

### 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

1. Introduction and examples. Mean function, autocovariance function (acvf), autocorrelation function (acf). Basic models: white noise, random walk, AR(1), MA(1). [1]
2. Basic structural model, exponential smoothing and related  models. [2]
3. Classical seasonal decomposition. [1]
4. Sample autocovariance and sample autocorrelation functions. Tests for white noise and their use for checking adequacy of models.   Outline of Box-Jenkins methodology. [1]
5. Linear filters: basic properties, backward shift operator, inverse filter.   Role of the roots of the characteristic polynomial. Differencing and seasonal differencing. [1]
6. Linear prediction. [2]
7. Stationary time series: acvf, acf, prediction, Yule-Walker equations, partial autocorrelation function (pacf).   Sample acvf and sample acf as estimators of acvf and acf, respectively.  [2]
8. Autoregressive (AR) models.   AR model building: identification, Yule-Walker estimation of parameters. Residuals. AIC criterion. Prediction and forecasting functions in AR models.  [2]
9. Moving average (MA) models and their acf. Seasonal MA models and their acf. Identification of MA models.   ARMA models. [1]
10. Integrated time series (I(1)). ARIMA and seasonal ARIMA models. Modelling seasonality and trend with ARIMA models. [2]
11. Estimation of parameters in ARMA models - basic ideas and properties.   Logarithmic and power transformations. [2]
12. Multivariate autoregression model.  Markov property.  Representation of univariate autoregression models in Markov form. [2]
13. Cointegrated time series. [1]
14. Other non-linear and/or non-stationary models - ARCH, threshold AR, bilinear. [2]
15. State space models and exponential smoothing: estimation, forecasting, assessing forecast accuracy, model selection. [6]
16. Dynamic regression models. [2]
17. Spectral analysis. [3]

### Textbooks

• Cryer, Jonathan D., Chan, Kung-Sik, Time Series Analysis With Applications in R, Series: Springer Texts in Statistics 2nd ed. 2008.
• Hyndman R.J., Koehler, A.B., Ord, J.K., Snyder, R.D., Forecasting with Exponential Smoothing: The State Space Approach, 2008.
• Shumway, Robert H., Stoffer, David S., Time Series Analysis and Its Applications, With R Examples, Springer Texts in Statistics, 2nd ed., 2006.
• Cowpertwait, Paul S.P., Metcalfe, Andrew V., Introductory Time Series with R, Series: Use R!, 2009,
• C Chatfiled, The analysis of Time Series: An Introduction, 5th ed., Chapman & Hall, CRC Press, 2001.
• P J Brockwell and R A Davis, An Introduction to Time Series and Forecasting, 2nd ed., Springer, 2002.

### Teaching and learning methods

Two lectures and one examples class each week. In addition students should expect to spend at least seven 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.