Approximate likelihood methods for stochastic differential equation models with high frequency sampling
Password: 202978
Date: 15 October 2020, Thursday
Time:10am 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.
Time:
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.
Video: