Module: Time Series Advanced

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Time Series Advanced
Module Code	MTH1076 (ITS: MS547)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	9	Credit Rating	7.5

Description

The module introduces the main concepts underlying the analysis of Time Series models, studying the stationarity of univariate and multivariate linear time series and some related models. The applications of this theory to dynamic economic modelling are also explored, especially in the context of inefficient markets and structural economic models, including model building and critical appraisal of the models. The analysis, development and appraisal of these financial models is among the principal distinctions between this module and corresponding Time Series modules delivered to undergraduate students (MS447, MS447A). Time Series.

Learning Outcomes

1. prove whether given time series models are weakly or strictly stationary and explain the suitability of using certain models in finance
2. establish the important properties of moving average models, and to apply them to model dynamically 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. develop nonstationary time series models of financial phenomena, and determine transformations which reduce them to stationary models
5. evaluate whether a given data set fits a particular stationary linear time series model and interpret the results of appropriate associated statistical tests
6. analyse vector autoregressive processes and determine their stationarity properties
7. propose multidimensional discrete time stochastic economic models which can be analysed and critiqued in the vector autoregressive process framework

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	32	Lectures
Tutorial	10	Working from supplied tutorial sheets
Laboratory	6	Practical computer labs – mixture of presentations and students working from supplied lab sheets
Independent Study	140	Self-study
Total Workload: 188

Section Breakdown
CRN	20801	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC1	Best Mark	N
Module Co-ordinator	John Appleby	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	n/a	10%	Week 8
In Class Test	Computer laboratory examination using the R programming language	20%	Week 11
Formal Examination	End-of-Semester Final Examination	70%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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. White noise process. Linear time series models. Short and long-range dependence. Wold's decomposition theorem. Partial autocorrelation function.

Moving average time series
Stationarity and invertibility of moving average models. Invertibility of general linear processes. Term structure of the autocovariance function and applications to modelling real estate and financial markets.

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.

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.

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.

Multivariate Processes
Multidimensional covariance function. Multidimensional white noise. Vector autogressive (VAR) processes. Stationarity and cointegration. Using VAR to model dynamic economic phenomena.

Further time series models
Properties and applications of bilinear, TAR and ARCH-type models

Indicative Reading List

Books:

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,

Articles:
None

Other Resources

None

Code assigned to this module is MS547.