This module is not currently running in 2024 to 2025.
This module will focus on basic features of stochastic processes and time series analysis. It includes: 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.
Total contact hours: 30
Private study hours: 120
Total study hours: 150
90% examination and 10% coursework
L. Breiman (1992) Probability. Philadelphia, PA: SIAM.
E. Cinlar (1975) Introduction to stochastic processes. Englewood Cliffs, N.J.:Prentice- Hal.
L. Breuer and D. Baum (2005) An introduction to queueing theory and matrix-analytic methods. Springer, Heidelberg
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 (1983) 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
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 will have a critical appreciation of the importance of statistics in different areas of current relevance;
2 will have an appreciation of actuarial areas of application in which statistical methods play a vital role, and of their importance;
3 will have an appreciation of the development of specialised methods of stochastic analysis for actuarial areas of application;
4 will be able to synthesise knowledge, and to appreciate links between disparate subject areas;
5 will appreciate the need to understand real world contexts in depth, and to devise appropriate stochastic models and methods.
The intended generic learning outcomes. On successfully completing the module students will be able to:
1 will have a systematic understanding of the role of logical argument;
2 will be able to evaluate research work critically;
3 will have technical expertise, particularly in relation to financial problems .
4 will have improved their key skills in written communication, numeracy and problem solving.
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