Markov Processes and Time Series

University of Cape Town

Course Description

  • Course Name

    Markov Processes and Time Series

  • Host University

    University of Cape Town

  • Location

    Cape Town, South Africa

  • Area of Study

    Statistics

  • Language Level

    Taught In English

  • Prerequisites

    Course entry requirements: STA2004F and STA2005S, MAM2000W is strongly recommended (linear algebra and advanced calculus modules).

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • Host University Units

    36
  • Recommended U.S. Semester Credits
    6
  • Recommended U.S. Quarter Units
    9
  • Overview

    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.

Course Disclaimer

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.