Registry
Module Specifications
Archived Version 2021 - 2022
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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 | |||||||||||||||||||||||||||||||||||||||||
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 |
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Indicative Content and
Learning Activities Stationary processesStrict and weak stationary, autocovariance function, integrated time series. Linear time series models. Wold's decomposition theorem. Partial autocorrelation function. CT6 xi 1-11Moving average time seriesStationarity and invertibility of moving average models. Invertibility of general linear processes. CT6 xi 1-11Linear autoregressive time seriesAR(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 SeriesReducing 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 -13Multidimensional and further time series modelsMultidimensional covariance function. Multidimensional white noise. Vector autogressive (VAR) processes. Stationarity and cointegration. Using VAR to model dynamic economic phenomena.Monte Carlo simulationPseudo-random number generation. Generation of random variates. Variance reduction. Simulation of time series. Efficiency of simulation. CT6 - [x] | |||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||||||
Programme or List of Programmes |
ACM | BSc in Actuarial Mathematics |
- See the module specification for MS447 in 2003 - 2004
- See the module specification for MS447 in 2004 - 2005
- See the module specification for MS447 in 2005 - 2006
- See the module specification for MS447 in 2006 - 2007
- See the module specification for MS447 in 2007 - 2008
- See the module specification for MS447 in 2008 - 2009
- See the module specification for MS447 in 2009 - 2010
- See the module specification for MS447 in 2010 - 2011
- See the module specification for MS447 in 2011 - 2012
- See the module specification for MS447 in 2012 - 2013
- See the module specification for MS447 in 2013 - 2014
- See the module specification for MS447 in 2014 - 2015
- See the module specification for MS447 in 2015 - 2016
- See the module specification for MS447 in 2016 - 2017
- See the module specification for MS447 in 2017 - 2018
- See the module specification for MS447 in 2018 - 2019
- See the module specification for MS447 in 2019 - 2020
- See the module specification for MS447 in 2020 - 2021
- See the module specification for MS447 in 2021 - 2022
- See the module specification for MS447 in 2022 - 2023
- See the module specification for MS447 in 2023 - 2024
- See the module specification for the current year