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Spectral methods for identifying scalar diffusions
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DOI：10.1016/S0304-4076(97)00107-3.png)
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Abstract
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This paper shows how to identify nonparametrically scalar stationary diffusions from discrete-time data. The local evolution of the diffusion is characterized by a drift and diffusion coefficient along with the specification of boundary behavior. We recover this local evolution from two objects that can be inferred directly from discrete-time data: the stationary density and a conveniently chosen eigenvalue-eigenfunction pair of the conditional expectation operator over a unit interval of time. This construction also lends itself to a spectral characterization of the over-identifying restrictions implied by a scalar diffusion model of a discrete-time Markov process. (C) 1998 Elsevier Science S.A. All rights reserved.
Keywords:
diffusion
identification
embeddability
continuous-time models in finance
spectral decomposition
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