MAS61005 Time Series

Note: This is an old module occurrence.

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Semester 2, 2020/21 15 Credits
Lecturer: Dr Georgios Chrysanthou Home page Timetable Reading List
Aims Outcomes Teaching Methods Assessment Full Syllabus

Time series are observations made sequentially in time, where an observation at one time point may be dependent on observations at previous time points. The course aims to give an introduction to modern methods of time series analysis and forecasting as applied in economics, engineering and the natural, medical and social sciences. The emphasis will be on practical techniques for data analysis, though appropriate stochastic models for time series will be introduced as necessary to give a firm basis for practical modelling. For the implementation of the methods the programming language R will be used.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.

Outline syllabus

  • Examples of time series. Purposes of analysis. Components (trend, cycle, seasonal, irregular). Stationarity and autocorrelation.
  • Approaches to time series analysis. Simple descriptive methods: smoothing, decomposition.
  • Differencing. Autocorrelation. Probability models for stationary series. Autoregressive models.
  • Moving average models. Partial autocorrelation. Invertibility. ARMA processes.
  • ARIMA models for non-stationary series. Identification and fitting. Diagnostics. Ljung-Box statistic, introduction to forecasting.
  • State space models. Filtering (Kalman filter), smoothing and forecasting.
  • Trend and seasonal state space models, time-varying regression. Estimation of hyperparameters, error analysis.

Office hours

Tuesday 12:00-13:00, Wednesday 13:00-14:00


  • introduce methods to uncover structure in series of observations made through time;
  • illustrate how models for time series may be constructed and studied, and how forecasts can be obtained;
  • demonstrate the application of time series analysis and forecasting methods using R ;
  • enhance students’ broader understanding of statistical methodology and develop their professional skills as applied statisticians.

Learning outcomes

  • describe various statistical models that can be used to analyse time series data; produce forecasts from time series data;
  • implement various time series methods using R, and interpret the results;
  • choose the most appropriate methodology for a time series analysis, from a set of possible methods;
  • carry out a time series analysis in a substantial case study, and communicate the key results/issues to a non-expert.

Teaching methods

There will be formal lectures, which will involve the explanation of theoretical concepts and their application to worked examples. The motivation, rationale, advantages and disadvantages of the various methods taught will be discussed as appropriate, with examples given of communicating issues to a lay audience. Detailed lecture notes will be provided, which students will be expected to study in their own time to assimilate the material. Lectures will include practical demonstrations of analysis using R. Students will work through set exercises in both theory and R implementation, and submit homework for marking, although this will not be part of the formal assessment. Students will undertake a project which will involve investigating the application of methods and concepts covered in the module in a substantial case study, and will be required to communicate their findings in a written report, at a level so that the key findings/issues can be understood by a non-expert reader.

20 lectures, no tutorials


One formal written examination (70%). All questions compulsory. One project (30%).

Full syllabus

  • Chapter 1: Examples of time series, definition of time series, aims of the module and overview of the methods.
  • Chapter 2: Descriptive methods for time series, using R in time series, time series plots, sample autocorrelation function, moving averages, the classical decomposition, lag plots.
  • Chapter 3: Probability models for stationary time series, definition of stationarity (strong and weak stationarity), autoregressive models (AR), infinite representation of AR models, stationarity and causality of AR models, moving average models (MA), invertibility of MA models, ARMA models, autocorrelation function and causality. Non-stationary ARMA models (ARIMA).
  • Chapter 4: Estimation and fitting of ARIMA models, Box-Jenkins approach, identification, fitting, maximum likelihood, diagnostics and residual analysis, model selection, examples. Forecasting, forecasting causal ARMA processes, 1-step ahead and i-step ahead forecasting, prediction intervals, forecasting non-stationary ARIMA and SARIMA processes.
  • Chapter 5: State space models, motivation and definition. Filtering (Kalman filter), smoothing and forecasting (Bayesian estimation). The local level model. Use of R for computing.
  • Chapter 6: Model specification and model performance. Examples of state space models: trend, seasonal and trend-seasonal state space models, time-varying regression and regression with autocorrelated errors. Estimation of hyperparameters. Error analysis and prior specification.

Reading list

Type Author(s) Title Library Blackwells Amazon
A Brockwell and Davies Introduction to Time Series and Forecasting 519.36 (B) Blackwells Amazon
A Shumway, R.H. and Stoffer, D.S Time series analysis and its applications : with R examples 519.55 (S) Blackwells Amazon
B Chatfield, C. The analysis of time series : an introduction 519.55 (C) Blackwells Amazon
B West and Harrison Bayesian Forecasting and Dynamic Models 519.42 (W) Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.


Mon 14:00 - 14:50 lecture   Blackboard Online
Tue 09:00 - 09:50 lecture   Blackboard Online