Statistics Across Campuses: Andrew Wood -- Approximate likelihood methods for stochastic differential equation

Approximate likelihood methods for stochastic differential equation models with high
frequency sampling 

Date: 15 October 2020, Thursday 

Time: 12pm 

Speaker: Prof Andrew Wood (ANU) 

Abstract: 

In most stochastic differential equation models the transition density is not available
in closed form.  This poses a serious challenge if we wish to adopt a likelihood-based
approach to estimation and inference.  The literature on this topic will be briefly
reviewed.  A two-step approach will then be described: (i) develop a small-time
Ito-Taylor approximation to the sample path; and (ii) apply the so-called epsilon
expansion to the Ito-Taylor approximation, leading to a closed-form approximation to the
transition density, which can in turn be used to construct an approximate likelihood.
My aim will be to discuss steps (i) and (ii) assuming no prior expertise.  The epsilon
expansion, which in a certain sense is a generalisation of the Edgeworth expansion, is
due to Cox and Reid (1987).  Some numerical results will be presented and various
further issues will be discussed.  

Link: https://anu.zoom.us/j/425258947?pwd=a2ovS1V0YmdqV0pROXZ0bGlsckVEZz09 Password:
202978