Higher-order difference and GLR tests for diffusion models

• Activity Number: 157
• Type: Invited
• Date/Time: Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Jianqing Fan*+
• Affiliation(s): Chinese University, Hong Kong/UNC-CH
• Keywords: Short term rate ; Higher order approximation ; GLR test ; Diffusion models

Abstract

Time-homogeneous diffusion model has been frequently employed for describing the stochastic dynamics of the underlying economic variables. To examine the impacts of higher-order discretizations, we develop general and explicit formulas for the asymptotic behaviors of both drift and diffusion estimators. We show that these estimators will reduce the numerical approximation errors in asymptotic biases, but their asymptotic variances escalate nearly exponentially with the order of discretization. The work of Stanton (1997) postulates an interesting question of whether the short-term rate drift is nonlinear. We develop ``Generalized Likelihood Ratio'' (GLR) tests to handle this kind of nonparametric testing question. Using this formal procedure, we show that the evidence against the linear drift of the short-term interest rates is weak, while against the family of popular models for the volatility of the short-term interest rates is very strong.