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Colloquium - Dept. Mathematics & Statistics presents Dr. Reg Kulperger of the Dept. of Statistical and Actuarial Sciences, University of Western Ontario

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  • Thu, 10/08/2015 - 3:00pm




Title: Nonlinear Time Series: GRARCH Type Process, Estimation and Applications

Abstract:

In mathematical finance both continuous and discrete time models are used. Continuous time models, in particular geometric Brownian motion (GBM), are easy to implement and use.   However they have certain assumptions. The log of GBM is Brownian motion with drift and so has independent Gaussian increments and is Markov.  Discrete time series models may still have     conditional Gaussian or other  driving noise, but might not be Markov.  However they are not as simple to implement for option pricing or hedging etc. Appropriate time series models for many    finance problems are not linear which have a constant conditional variance. One very useful class of models is GARCH type models.

Estimation, and their asymptotics are well studied, but there are still many not completely solved problems in this class of models.  We discuss some of these, in particular the simplest GARCH in mean.  Some additional time series structure, such as multivariate processes are       discussed, and the problem of these having a very large number of parameters, and without an   explicit simple parameter space.

 



Dina Labelle
mthsta1@uwindsor.ca
519-253-3000 ext.3016