A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions

• Main Authors: BANDI, Federico, PHILLIPS, Peter C. B.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2007
• Subjects: Diffusion; Drift; Local time; Parametric estimation; Stochastic differential equation; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/281; https://ink.library.smu.edu.sg/context/soe_research/article/1280/viewcontent/SimpleApproach_ParametricEstimation_2007.pdf
• Institution: Singapore Management University

A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic differential equations. We specify a parametric class of diffusions and estimate the parameters of interest by minimizing criteria based on the integrated squared difference between kernel estimates of the drift and diffusion functions and their parametric counterparts. The procedure does not require simulations or approximations to the true transition density and has the simplicity of standard nonlinear least-squares methods in discrete time. A complete asymptotic theory for the parametric estimates is developed. The limit theory relies on infill and long span asymptotics and is robust to deviations from stationarity, requiring only recurrence.