STA3041F - Stochastic Processes & Time Series

Course Outline:

This course forms part of the third-year major in Mathematical Statistics. It consists of two modules namely Stochastic Processes and Time Series Analysis. The Stochastic Processes module is aimed at providing introductory theory and basic applications of stochastic processes in financial modelling whilst the Time Series module introduces students to the foundations of the Box-Jenkins methodology with the intention of applying the methodology using statistical software. Details of the module content are as follows: Stochastic processes: The module covers the general theory underlying stochastic processes and their classifications, definitions and applications of discrete Markov chains. Branching processes are examined with an emphasis on analysing probability of extinction/survival. The module also covers both discrete and continuous time counting processes for purposes constructing forecasts and backcasts. Finally, a detailed introduction to homogeneous and non-homogeneous Poisson processes is given. Time series analysis: The module covers various topics including 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 cointegration.