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Module Specifications

Archived Version 2016 - 2017

Module Title Time Series (Intermediate)
Module Code MS447
School School of Mathematical Sciences

Online Module Resources

Module Co-ordinatorProfessor John ApplebyOffice NumberX133
NFQ level 8 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
Description

The module introduces the main concepts underlying the analysis of Time Series models, studying the stationarity of linear time series and some related models. It also includes an introduction to Monte Carlo simulation and introduces dynamic discrete time financial models. It covers the syllabus of the Time Series part of the Institute of Actuaries Core Technical subject CT6, giving students of actuarial programmes the opportunity to be recommended for an exemption from the professional examination in this Core Technical subject. The end of semester examination is of two hours’ duration, and has more limited choice than the examination in MS447A, which is set for financial mathematics students.

Learning Outcomes

1. prove whether given time series models are weakly or strictly stationary
2. establish the important properties of moving average models, and to apply them to model financial phenomena
3. characterise the class of linear autoregressive models which possess unique attracting stationary solutions, and to apply these processes to model financial phenomena
4. reduce time series data and models to the stationary case, and to decide whether certain data sets fit a given stationary linear time series model
5. analyse vector autoregressive models
6. establish the validity of important general methods for generating random variates, to apply these methods, and analyse their efficiency



Workload Full-time hours per semester
Type Hours Description
Lecture36Lectures
Tutorial12Tutorial
Independent Study140Self study
Total Workload: 188

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Stationary processes
Strict and weak stationary, autocovariance function, integrated time series. Linear time series models. Wold's decomposition theorem. Partial autocorrelation function. CT6 xi 1-11

Moving average time series
Stationarity and invertibility of moving average models. Invertibility of general linear processes. CT6 xi 1-11

Linear autoregressive time series
AR(p) time series. Characterisation of stationarity. Stationary solutions and uniqueness. Applications to volatility and interest rate modelling. ARMA(p,q) models, in particular ARMA(1,1). ARIMA models.

Data analysis of Time Series
Reducing time series to stationary series. Box-Jenkins method for fitting linear time series. Statistical testing for white noise, moving average, autoregressive models. CT6 - [ix] 12 -13

Multidimensional and further time series models
Multidimensional covariance function. Multidimensional white noise. Vector autogressive (VAR) processes. Stationarity and cointegration. Using VAR to model dynamic economic phenomena.

Monte Carlo simulation
Pseudo-random number generation. Generation of random variates. Variance reduction. Simulation of time series. Efficiency of simulation. CT6 - [x]

Assessment Breakdown
Continuous Assessment25% Examination Weight75%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Reassessment Requirement
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
Unavailable
Indicative Reading List

  • J. Franke, W. Hardle, C. Hafner.: 2003, Statistics of Financial Markets, Springer,
  • P. Brockwell, R. Davis.: 1991, Time Series: Theory and Methods, Springer,
  • C. Chatfield: 2004, The Analysis of Time Series: An introduction, 6th ed., Chapman and Hall,
  • Institute of Actuaries: 2011, Combined Materials Pack, CT6,
Other Resources

None
Programme or List of Programmes
ACMBSc in Actuarial Mathematics
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