Browsing by Author "Lapham, Brendon M"

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    Hawkes processes and some financial applications
    (2014) Lapham, Brendon M; MacDonald, Iain L
    The self-exciting point process, which is now more commonly known as the Hawkes process, is a model for a point process on the real line introduced by Hawkes (1971). The distinguishing feature of such processes is that they allow all past `events' to affect the intensity function at the current time. Over the years such processes have been applied in seismology and neurophysiology in particular, and in more recent years there have been significant financial applications. In almost all of these applications, the route used to find the maximum likelihood estimates (MLEs) is direct numerical maximisation (DNM) of the likelihood. An EM algorithm, which makes use of the Poisson cluster process interpretation of the Hawkes process, is an alternative route to the MLEs. This particular EM algorithm has received attention in the literature and has been claimed to have advantages over DNM of the likelihood. We carry out a simulation study for a simple Hawkes process to clarify statements made in the literature about these advantages. For the simple Hawkes process models that we consider, DNM of the likelihood is the preferable route to finding the MLEs. We then use DNM of the likelihood to _t marked Hawkes process models to South African asset data. These applications to South African data include the modelling of extreme asset returns and the forecasting of conditional value-at-risk (VaR) and expected shortfall (ES). The models investigated include mostly models found in the literature, but also include some variations introduced here. In a backtesting exercise, we compare the conditional VaR and ES forecasts found by using the marked Hawkes process models with those found via some nonstandard stochastic volatility (SV) models. We find that the marked Hawkes process models give mostly competitive forecasts of conditional VaR and ES when compared with the nonstandard SV models.
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    Modelling Multivariate Nonlinear Vaccine Induced Immune Responses
    (2020) Lapham, Brendon M; Little, Francesca
    Interpretable statistical models for multivariate vaccine induced immune response data are important as they provide a rigorous means of deciding which vaccine candidates should be advanced in the clinical trials process. We consider applications of several different statistical models to a vaccine data set which contains multivariate immune responses for several novel Tuberculosis vaccines and the current BCG vaccine. The immune responses in the data set have several features which the models need to account for. In particular, the models need to account for the multivariate repeated measures for the subjects, the nonlinear profiles of the immune responses, and the zero-inflated skew distributions of the immune responses. We find that Tweedie multivariate generalised linear mixed effect and latent variable models with cubic B-splines perform well for this data set relative to linear, nonlinear, and univariate Tweedie generalised linear mixed effect models. In addition, the Tweedie multivariate generalised linear mixed effect and latent variable models have several advantages over the other models we consider and are also capable of interpretation; importantly, we are able to draw clinical conclusions about which novel TB vaccine candidates appear to be the most promising.