In this paper, we propose a nonparametric identification and estimation procedure for an ltd diffusion process based on discrete sampling observations. The nonparametric kernel estimator for the diffusion function developed in this paper deals with general ltd diffusion processes and avoids any functional form specification for either the drift function or the diffusion function. It is shown that under certain regularity conditions the nonparametric diffusion function estimator is pointwise consistent and asymptotically follows a normal mixture distribution. Under stronger conditions, a consistent nonparametric estimator of the drift function is also derived based on the diffusion function estimator and the marginal density of the process. An application of the nonparametric technique to a short-term interest rate model involving Canadian daily 3-month treasury bill rates is also undertaken. The estimation results provide evidence for rejecting the common parametric or semiparametric specifications for both the drift and diffusion functions.
This article examines the class of continuous-time stochastic processes commonly known as af ne diffusions (AD's) and af ne jump diffusions (AJD's). By deriving the joint characteristic function, we are able to examine the statistical properties as well as develop an ef cient estimation technique based on empirical characteristic functions (ECF's) and a generalized method of moments (GMM) estimation procedure based on exact moment conditions. We demonstrate that our methods are particularly useful when the diffusions involve latent variables. Our approach is illustrated with a detailed examination of a continuous-time stochastic volatility (SV) model, along with an empirical application using S&P 500 index returns.
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