Unit information: Time Series Analysis in 2020/21

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. Imogen Noad
Open unit status	Not open
Pre-requisites	MATH10013 Probability and Statistics, MATH10011 Analysis, MATH10012 ODEs, Curves and Dynamics, and MATH11005 Linear Algebra and Geometry
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

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.

Intended Learning Outcomes

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

Teaching Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

90% Timed, open-book examination 10% Coursework

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.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Reading and References

Recommended

• Brockwell, P. J., & Davis, R. A. 2016. Introduction to Time Series and Forecasting, Springer, https://doi.org/10.1007/978-3-319-29854-2.
• Chatfield, C. 2004. The Analysis of Time Series: An Introduction, 6th edition, Chapman & Hall/CRC.
• Hyndman, R. J., & Athanasopoulos, G. (2018) Forecasting: principles and practice, 2nd edition, OTexts: Melbourne, Australia. OTexts.com/fpp2.