Statistical inference for stochastic models

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The proposed research topics are aspects of my continuing research program in estimation and inference for stochastic modeling. The nonlinear times series models are of the GARCH family. We will study parameter identification, estimation and diagnostic tools for these processes. In additional we will study an application to portfolio optimization. We will also study GARCH in mean processes. The portfolio question is quite important as the present methodology assumes returns are independent, and often with a normal distribution. Independence and the normality assumptions bias measures of risk and in general greatly underestimates risk, such as value at risk. This method will address this problem.We will study simulation of spatial processes in a high performance computing (HPC) environment. At present HPC has been applied to deterministic spatial functions, but not to stochastic spatial processes, which in general have a spatial or neighbourhood interaction component. The later is important not just for our motivating application, but for many applications, such as ecology and environmental applications where space or location is a key feature.We will also study estimation for diffusions using higher order Ito-Taylor methods, a periodic Ornstein-Uhlenbeck process applied to commodity oil and gas markets, and a multi prey competing species model. The first two diffusion applications are motivated by and will use experimental data and a European natural gas commodity data set.