Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Time Series
Module Code	MS447
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: John Appleby Semester 2: John Appleby Autumn: John Appleby
Module Teacher	John Appleby
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. 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. 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*
Lecture	36	Lectures
Tutorial	12	Tutorial
Independent learning time	140	Self 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 Assessment	25%	Examination Weight	75%

Course Work Breakdown
Type	Description	% of total	Assessment Date
In Class Test	n/a	15%	Week 10
Assignment	Unseen problems at a level of difficulty above tutorial or examination questions.	10%	Week 11

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
This module is category 3

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

Array

Programme or List of Programmes

ACM

BSc Actuarial Mathematics

BSSA

Study Abroad (DCU Business School)

BSSAO

Study Abroad (DCU Business School)

ECSA

Study Abroad (Engineering & Computing)