Likelihood Inference and Jump Detection for Non-Linear Jump Diffusions With State-Dependent Intensity

Dr Etienne Pienaar will present the Department of Statistical Science seminar with a talk entitled, "Likelihood Inference and Jump Detection for Non-Linear Jump Diffusions With State-Dependent Intensity".  

Jump diffusion processes can be seen as a generalisation of standard diffusion processes whereby the trajectory of the underlying diffusion process is allowed to be perturbed by a jump process. Unfortunately, the analysis of diffusion models in general is extremely difficult, due in most part to the intractability of the probabilistic dynamics of such processes, with only a few simple models having analytically tractable transitional densities. For these purposes, we develop a method for approximating the transitional densities of a class of time-inhomogeneous jump diffusions with state-dependent and/or stochastic intensity. By deriving a system of equations that govern the evolution of the moments of the process, we are able to approximate the transitional density through a density factorization that contrasts the dynamics of the jump diffusion with that of its jump free counterpart. Within this framework, we can thus calculate accurate and computationally efficient approximations to the likelihood function of a diffusion model of a discretely observed time series. We demonstrate the workings of methodology and analyse a real-world dataset, showing how the methodology can be used to detect jumps in financial time series. 

Date: 
Monday, August 28, 2017 - 13:00
Venue: 

PD Hahn Building Lecture Theatre 3, Upper Campus, UCT

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