Unit name | Time Series Analysis |
---|---|

Unit code | MATH33800 |

Credit points | 20 |

Level of study | H/6 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Dr. Kley |

Open unit status | Not open |

Pre-requisites |
MATH11300 Probability 1 and MATH11400 Statistics 1 (or MATH10013 Probability and Statistics), MATH10003 Analysis 1A and MATH10006 Analysis 1B (or MATH10011 Analysis), MATH 11007 Calculus 1 (or MATH10012 ODEs, Curves and Dynamics), and MATH11005 Linear Algebra and Geometry |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

**Unit Aims**

This unit provides an introduction to time series analysis mainly from the statistical point of view but also covers some mathematical and signal processing ideas.

**Unit Description**

Time series are observations on variables collected through time. For example two well-known time series are daily temperature readings and hourly stock prices. Time series data are widely collected in many fields: for example in the pure sciences, medicine, marketing, economics and finance to name but a few. Time series data are different to the usual statistical data in that the observations are ordered in time and usually correlated. The emphasis is on understanding, modelling and forecasting of time- series data in both the time, frequency and time-frequency domains.

Time series specialists are valued by a wide range of organisations who collect time series data (see list above). This course will equip you with a formidable collection of skills and knowledge that are highly valued by employers. Alternatively, the course would give you a good grounding if you wished to develop time series methods for a higher degree (e.g. PhD).

**Relation to Other Units**

As with units Linear and Generalised Linear Models and Multivariate Analysis, this course is concerned with developing statistical methodology for a particular class of problems.

Learning Objectives

The students will be able to:

- carry out an initial data analysis of time-series data and be able to identify and remove simple trend and seasonalities;
- compute the correlogram and identify various features from it (eg short term correlation, alternating series, outliers);
- define various time-series probability models;
- construct time series probability models from data and verify model fits;
- define the spectral density function and understand it as a distribution of energy in the frequency domain;
- compute the periodogram and smoothed versions;
- analyse bivariate processes.

Transferable Skills

Use of R for advanced statistical time-series analyses. Enhanced mathematical modelling skills Problem solving

The teaching methods consist of

- 30 standard lectures.
- Regular problem sheets which will: develop theoretical understanding of the lectures and extra-lecture topics; relate the lectures to real practical problems arising in time-series analysis and signal processing. The students will develop a basic knowledge of time-series analysis within the R package.
- Detailed solution sheets will be released approximately two weeks after the problem sheets.

Three problem sheets will count towards both assessment and credit points. It will be made clear in the lectures and on the sheets which count for assessment and credit points. Other problem sheets will be set: they will be marked but it is not compulsory to hand these in (although it would obviously be to your benefit as you would receive feedback).

94% Examination and 6% Homework Assignments.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

**Recommended**

- Christopher Chatfield,
*The Analysis of Time Series: An Introduction*, Chapman and Hall, 1984 - Peter Diggle,
*Time Series: A Biostatistical Introduction*, Oxford University Press, 1990 - G. J. Janacek,
*Practical Time Series,*Arnolds Texts in Statistics, 2001