Time Series Modelling and Simulation - MAST6390

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Module delivery information

Location Term Level1 Credits (ECTS)2 Current Convenor3 2024 to 2025
Spring Term 6 15 (7.5) Alfred Kume checkmark-circle


Stationary Time Series: Stationarity, autocovariance and autocorrelation functions, partial autocorrelation functions, ARMA processes.
ARIMA Model Building and Testing: estimation, Box-Jenkins, criteria for choosing between models, diagnostic tests for residuals of a time series after estimation.
Forecasting: Holt-Winters, Box-Jenkins, prediction bounds.
Testing for Trends and Unit Roots: Dickey-Fuller, ADF, structural change, trend-stationarity vs difference stationarity.
Seasonality and Volatility: ARCH, GARCH, ML estimation.
Multiequation Time Series Models: transfer function models, vector autoregressive moving average (VARM(p,q)) models, impulse responses.
Spectral Analysis: spectral distribution and density functions, linear filters, estimation in the frequency domain, periodogram.
Simulation: generation of pseudo-random numbers, random variate generation by the inverse transform, acceptance rejection. Normal random variate generation: design issues and sensitivity analysis.
This module will cover a number of syllabus items set out in Subject CS2 published by the Institute and Faculty of Actuaries. This is a dynamic syllabus, changing regularly to reflect current practice.


Contact hours

Total contact hours: 46
Private study hours: 104
Total study hours: 150

Method of assessment

Level 6
Assessment 1 (10-15 hrs) 15%
Assessment 2 (10-15 hrs) 15%
Examination (2 hours) 70%

Reassessment Methods

Indicative reading

Enders, W. (2004), Applied Econometric Time Series, New York: Wiley.
Brockwell, P.J., and Davis, R. A. (2002), Introduction to Time Series Analysis and Forecasting, New York: Springer-Verlag.
Morgan, B. J. T. (1984), Elements of Simulation, London: Chapman & Hall/CRC.
Study notes published by the Actuarial Education Company for Subject CS2.

See the library reading list for this module (Canterbury)

Learning outcomes

The intended subject specific learning outcomes. On successfully completing this module students will be able to:
1 demonstrate systematic understanding of key aspects of time series modelling and simulation;
2 demonstrate the capability to deploy established approaches accurately to analyse and solve problems using a reasonable level of skill in calculation and manipulation of
the material in the following areas: ARIMA and GARCH time series models including those modelling seasonality, main methods for simulating random variates;
3 apply key aspects of time series modelling in well-defined contexts, showing judgement in the selection and application of tools and techniques.

The intended generic learning outcomes. On successfully completing this module students will be able to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly and communicate technical material competently;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make competent use of information technology skills such as online resources (Moodle);
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.


  1. Credit level 6. Higher level module usually taken in Stage 3 of an undergraduate degree.
  2. ECTS credits are recognised throughout the EU and allow you to transfer credit easily from one university to another.
  3. The named convenor is the convenor for the current academic session.
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