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Module Specifications

Archived Version 2021 - 2022

Module Title
Module Code

Online Module Resources

NFQ level 9 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

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). The module also includes an introduction to Monte Carlo simulation and applications to simulating Time Series. The end of semester examination will be of three hours’ duration and will require students to answer all questions on the paper.

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
8. establish the validity of important general methods for generating random variates, to apply and appraise these methods to modeling random financial phenomena, and to design and assess optimally efficient algorithms for generating these random variables.

Workload Full-time hours per semester
Type Hours Description
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. 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.

Nonstationary time series and data analysis of time series
Modelling nonstationary random economic phenomena. Reducing nonstationary time series to stationary series: principles and practice. Box-Jenkins method for fitting linear time series. Statistical testing for white noise, moving average, autoregressive models. Forecasting.

Multidimensional time series models
Multidimensional covariance function. Multidimensional white noise. Vector autogressive (VAR) processes. Stationarity and cointegration. Developing and analysing dynamic economic models using VAR processes. Properties and applications of ARCH type models.

Monte Carlo simulation
Pseudo-random number generation. Generation of random variates. Simulation of time series. Reliability and efficiency of simulation.

Assessment Breakdown
Continuous Assessment% Examination Weight%
Course Work Breakdown
TypeDescription% of totalAssessment Date
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
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,
Other Resources

Programme or List of Programmes