Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data
Andrew W. Lo
Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER); Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)
NBER Working Paper No. t0059
In this paper, we consider the parametric estimation problem for continuous time stochastic processes described by general first-order nonlinear stochastic differential equations of the Ito type. We characterize the likelihood function of a discretely-sampled set of observations as the solution to a functional partial differential equation. The consistency and asymptotic normality of the maximum likelihood estimators are explored, and several illustrative examples are provided.
Number of Pages in PDF File: 32
Date posted: June 27, 2007