UBC Theses and Dissertations
Kernel estimation of the drift coefficient of a diffusion process in the presence of measurement error Lee, Wooyong
Diffusion processes, a class of continuous-time stochastic processes, can be used to model time-series data observed at discrete time points. A diffusion process can be completely characterized by two functions, called the drift coefficient and the diffusion coefficient. For the nonparametric estimation of these two functions, Bandi and Phillips (2003) proved consistency and asymptotic normality of Nadaraya-Watson kernel estimators of the drift and the diffusion coefficient. In some cases, we observe the time-series data with measurement error. For instance, it is a well-known fact that we observe the financial time-series data with measurement errors (Zhou, 1996). For the nonparametric estimation of the drift and the diffusion coefficients in the presence of measurement error, some works are done for the estimation of integrated volatility, which is the integral of the diffusion coefficient over a fixed period of time, but little work exists on the estimation of the drift and the diffusion coefficients themselves. In this thesis, we focus on the estimation of the drift coefficient, and we propose a consistent and asymptotically normal Nadaraya-Watson type kernel estimator of the drift coefficient in the presence of measurement error.
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