SPECTRAL METHODS FOR IDENTIFYING SCALAR DIFFUSIONS

This paper shows how to identify nonparametrically scalar stationary d iffusions from discrete-time data. The local evolution of the diffusio n is characterized by a drift and diffusion coefficient along with the specification of boundary behavior. We recover this local evolution f rom two objects that can be inferred directly from discrete-time data: the stationary density and a conveniently chosen eigenvalue-eigenfunc tion pair of the conditional expectation operator over a unit interval of time. This construction also lends itself to a spectral characteri zation of the over-identifying restrictions implied by a scalar diffus ion model of a discrete-time Markov process. (C) 1998 Elsevier Science S.A. All rights reserved.