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Module Specifications

Archived Version 2010 - 2011

Module Title Time Series
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

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. It cover the syllabus of the Time Series part of the Institute and Faculty of Actuaries Core Technical subject CT6, giving students of actuarial programmes an opportunity to be recommened for an exemption from the professional examination in this Core Technical subject. It is an advanced level undergraduate course with a substantial theoretical component, and provides the platform for further advanced courses in financial econometrics.

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. model multidimensional discrete time stochastic economic phenomena, and analyse these models as vector autoregressive models
6. analyse nonlinear time series models from the class of ARCH models
7. 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
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. Applications to modelling inefficient financial markets 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. Forecasting. 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. Properties and applications of ARCH type models.

Monte Carlo simulation
Pseudo-random number generation. Generation of random variates. Variance reduction. Simulation of time series. Reliability 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
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,
Other Resources

786, Printed notes, The Actuarial Education Company, 2009, CT6 Course Notes, ACTED,
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