Non-parametric econometric methods for continuous-time diffusion models
Continuous-time diffusion models are widely used in economics and finance to describe the dynamics of economic variables such as asset prices, interest rates, and exchange rates. Unfortunately, economic theory puts only few restrictions on the specification of the processes, and as a consequence many parametric diffusion models coexist in the literature. To mitigate the risk caused by misspecification, several authors have proposed non-parametric methods to estimate diffusion processes. However, the fundamental question whether the process is actually a diffusion still remains. My doctoral dissertation is the first to provide a statistical method to directly answer this question. I develop a new non-parametric testing procedure to tell whether the underlying continuous-time Markov process is a diffusion, and apply it to short-term interest rates and foreign exchange rates. I also propose new semi-parametric and non-parametric estimators for diffusion processes and derive asymptotic results under fairly weak conditions.