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Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

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Module Title
Module Code (ITS)
Faculty School
Module Co-ordinatorSemester 1: John Appleby
Semester 2: John Appleby
Autumn: John Appleby
Module TeachersJohn Appleby
Mingchuan Zhao
NFQ level 8 Credit Rating
Pre-requisite Not Available
Co-requisite Not Available
Compatibles Not Available
Incompatibles Not Available
None
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



Workload Full-time hours per semester
Type Hours Description
Lecture32Lectures
Tutorial10Working from supplied tutorial sheets
Laboratory6Practical computer labs – mixture of presentations and students working from supplied lab sheets
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. [CS2 – 2.1.1-3]

Moving average time series
Linear 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 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). Markov property of AR-type models. [CS2 – 2.1.4-5,2.1.9, 2.2.3]

Non-stationarity and ARIMA models
ARIMA 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 models
Fitting 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 models
Multidimensional 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 Models
Properties and applications of bilinear, TAR and ARCH-type models [CS2 – 2.2.2]

Assessment Breakdown
Continuous Assessment% Examination Weight%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class Testn/a10%Week 8
AssignmentComputer lab exam using the R programming language (90 minutes)20%Week 11
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, Chapman and Hall,
Other Resources

None

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