University of Kent s3

UNIVERSITY OF KENT

Confirmation that this version of the module specification has been approved by the School Graduate Studies Committee:

01 March 2015

MODULE SPECIFICATION

1. Title of the module MA885, Stochastic Processes and Time Series 2. School or partner institution which will be responsible for management of the module School of Mathematics, Statistics and Actuarial Science 3. Start date of the module Autumn 2015 (update)

4. The number of students expected to take the module 7

5. Modules to be withdrawn on the introduction of this proposed module and consultation with other relevant Schools and Faculties regarding the withdrawal None.

6. The level of the module (e.g. Certificate [C], Intermediate [I], Honours [H] or Postgraduate [M]) Honours [H]

7. The number of credits and the ECTS value which the module represents 15 (7.5 ECTS credits)

8. Which term(s) the module is to be taught in (or other teaching pattern) Both terms 9. Prerequisite and co-requisite modules MA881, Probability and Classical Inference, is a co-requisite 10. The programmes of study to which the module contributes MSc in Statistics 11. The intended subject specific learning outcomes On successful completion of this module, students

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11.1 will have a critical appreciation of the importance of statistics in different areas of current relevance [A6, B1]; 11.2 will have an appreciation of actuarial areas of application in which statistical methods play a vital role, and of their importance [B3]; 11.3 will have an appreciation of the development of specialised methods of stochastic analysis for actuarial areas of application [A6]; 11.4 will be able to synthesise knowledge, and to appreciate links between disparate subject areas [A2, B2]; 11.5 will appreciate the need to understand real world contexts in depth, and to devise appropriate stochastic models and methods [A1, A4, C1, C2].

12. The intended generic learning outcomes On successful completion of this module, students 12.1 will have a systematic understanding of the role of logical argument [A5, B4]; 12.2 will be able to evaluate research work critically [B8]; 12.3 will have technical expertise, particularly in relation to financial problems [D7]. 12.4 will have improved their key skills in written communication, numeracy and problem solving [D4] 13. A synopsis of the curriculum Markov chains on discrete state spaces, communication classes, transience and recurrence, positive recurrence, stationary distributions. Markov processes on discrete state spaces, exponential distribution, embedded Markov chain, transition graphs, infinitesimal generator, transition probabilities, stationary distributions, skip-free Markov processes. Stationary Time Series: Stationarity, Autocovariance and autocorrelation functions, Partial autocorrelation functions, ARMA processes. ARIMA Model Building and Testing: Estimation, Box Jenkins, Criteria for choosing between models, Diagnostic tests for the residuals of a time series after estimation. Forecasting: Holt-Winters, Box-Jenkins, Prediction bounds. 14. Indicative Reading List L. Breiman (1992) Probability. Philadelphia, PA: SIAM. L. Breuer and D. Baum (2005) An introduction to queueing theory and matrix-analytic methods. Springer,Heidelberg. E. Cinlar (1975) Introduction to stochastic processes. Englewood Cliffs, N.J.:Prentice-Hal. S. Karlin and H. M. Taylor (1975) A first course in stochastic processes. 2nd ed., New York: Academic Press. S. Ross (1970) Applied Probability Models with Optimization Applications. Dover, New York. S. Ross (1993) Stochastic Processes. John Wiley & Sons, New York. W. Enders (2004) Applied Econometric Time Series New York: Wiley. P.J. Brockwell and R.A. Davis (2002) Introduction to time series and forecasting. Springer. 15. Learning and Teaching Methods, including the nature and number of contact hours and the total study hours which will be expected of students, and how these relate to achievement of the intended module learning outcomes Hours of study and contact hours. No. of contact hours: 30 lectures (each of an hour) Home study: 120 Total study hours: 150 About 3 exercise sheets are set and discussed. All of these exercises are intended to reinforce the lecture material and to apply the concepts taught to practical problems. Student study hours would be distributed between consolidation of lecture material, the working of exercises on exercise sheets, assessed exercises, and exam preparation.

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16. Assessment methods and how these relate to testing achievement of the intended module learning outcomes Assessment: The unit is assessed by examination (80%) and by continuous assessment (20%). Continuous Assessment: This will consist of several open-book written assessments which are completed by Students outside contact hours. These consist of questions and numerical problems which will test the learning outcomes 11.1-11.5 and 12.1-12.4. Examination: A 2-hour written examination in the Summer term that will consist of multi- part questions requiring a mix of long and short answers to test at varying levels the proficiency of the learning outcomes 11.1-11.5 and 12.1-12.4. 17. Implications for learning resources, including staff, library, IT and space The module will be taught by an existing member of staff from the Statistics Group of the School of Mathematics, Statistics and Actuarial Science. The recommended texts are currently available in the library. Therefore there should be minimal overall impact on the above resources. 18. The School recognises and has embedded the expectations of current disability equality legislation, and supports students with a declared disability or special educational need in its teaching. Within this module we will make reasonable adjustments wherever necessary, including additional or substitute materials, teaching modes or assessment methods for students who have declared and discussed their learning support needs. Arrangements for students with declared disabilities will be made on an individual basis, in consultation with the University’s disability/dyslexia support service, and specialist support will be provided where needed. 19. Campus(es) or Centre(s) where module will be delivered: Canterbury Campus

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