Markov Processes and Time Series

Course outline:
This course forms part of the third year major in Mathematical Statisitics. It consists of two modules. The aim of the Stochastic Processes module is to provide grounding for theory and basic applications in financial modelling while the aim of the Time Series module is to introduce students to the foundations of the Box-Jenkins methodology with the intention of applying the techniques using statistical software. The content of the modules are as follows:
Stochastic processes: The modules cover the general theory underlying stochastic processes and their classifications, definitions and applications of discrete Markov chains. Branching processes are examined for extinction or survival. Probabilities associated with multiple events are derived and applications presented. Counting processes in discrete and continuous time are modelled with a view to establishing methods of forecast and backcast. Ruin theory and reinsurance themes are insurance of continuous time processes. Ruin and loss are considered in a framework covering single claims for losses or insured events. Students are also introduced to run-off triangles.
Time series analysis: Topics that are covered include: global and local models of dependence, stationary ARMA processes, unit root processes as well as a brief introduction to univariate Volatility models as well as cointergration.