Module Specifications.
Current Academic Year 2024 - 2025
All Module information is indicative, and this portal is an interim interface pending the full upgrade of Coursebuilder and subsequent integration to the new DCU Student Information System (DCU Key).
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Date posted: September 2024 No Banner module data is available
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Description The module introduces the main concepts underlying the analysis of Time Series models: it concerns the stationarity of linear time series and some related models. It is an advanced level undergraduate course with a substantial theoretical component as well as hands-on experience in fitting data to models using computers. The module does not render students eligible for exemptions from professional actuarial examinations, and therefore assessment differs somewhat from a corresponding module delivered to actuarial students (MS447). | |||||||||||||||||||||||||||||||||||||||||||
Learning Outcomes 1. prove whether given time series models are weakly or strictly stationary 2. establish the important properties of moving average models 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 fit these data sets to the appropriate linear time series model using statistical packages 5. Model multidimensional discrete time stochastic economic phenomena, and analyse these models as vector autoregressive models 6. Analyse other important non-ARIMA time series models | |||||||||||||||||||||||||||||||||||||||||||
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. [CS2 – 2.1.1-3]Moving average time seriesLinear difference equations. Stationarity and invertibility of moving average models. Invertibility of general linear processes. Operator algebra. Applications to modelling inefficient financial markets [CS2 – 2.1.4-6, 2.2.4]Linear 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). Markov property of AR-type models. [CS2 – 2.1.4-5,2.1.9, 2.2.3]Non-stationarity and ARIMA modelsARIMA models. Transient nonstationarity. Stability of stationarity under differencing. Reducing time series to stationary series. Economic modelling of bubbles and seasonal behaviour. [CS2 – 2.1.5, 2.2.4]Fitting and Prediction in ARIMA modelsFitting and Prediction in ARIMA models Box-Jenkins method for fitting linear time series. Statistical testing for white noise, moving average, autoregressive models. The prediction operator and forecasting. [CS2 – 2.2.1, 2.2.4]Multidimensional and further time series modelsMultidimensional covariance function. Multidimensional white noise. Vector autogressive (VAR) processes. Stationarity and cointegration. Using VAR to model dynamic economic phenomena. [CS2 – 2.1.7-9, 2.2.3-4]Further Time Series ModelsProperties and applications of bilinear, TAR and ARCH-type models [CS2 – 2.2.2] | |||||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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