Spectral methods for identifying scalar diffusions

Lars Peter Hansen; José Alexandre Scheinkman; Nizar Touzi

doi:10.1016/S0304-4076(97)00107-3

Spectral methods for identifying scalar diffusions

Lars Peter Hansen, José Alexandre Scheinkman, Nizar Touzi

Finance and Risk Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	1-32
Number of pages	32
Journal	Journal of Econometrics
Volume	86
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4076(97)00107-3
State	Published - Jun 15 1998

Keywords

Continuous-time models in finance
Diffusion
Embeddability
Identification
Spectral decomposition

ASJC Scopus subject areas

Applied Mathematics
Economics and Econometrics

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10.1016/S0304-4076(97)00107-3

Cite this

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title = "Spectral methods for identifying scalar diffusions",

abstract = "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.",

keywords = "Continuous-time models in finance, Diffusion, Embeddability, Identification, Spectral decomposition",

author = "Hansen, {Lars Peter} and Scheinkman, {Jos{\'e} Alexandre} and Nizar Touzi",

note = "Funding Information: We have benefitted greatly from conversations with Yacine Ait-Sahalia, Marine Carrasco, Xiaohong Chen, Tim Conley, Erzo Luttmer and Andrei Taskin, and from comments by an anonymous referee. Hansen and Scheinkman both received NSF funding in support of this research. ",

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AU - Hansen, Lars Peter

AU - Scheinkman, José Alexandre

AU - Touzi, Nizar

N1 - Funding Information: We have benefitted greatly from conversations with Yacine Ait-Sahalia, Marine Carrasco, Xiaohong Chen, Tim Conley, Erzo Luttmer and Andrei Taskin, and from comments by an anonymous referee. Hansen and Scheinkman both received NSF funding in support of this research.

PY - 1998/6/15

Y1 - 1998/6/15

N2 - 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.

AB - 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.

KW - Continuous-time models in finance

KW - Diffusion

KW - Embeddability

KW - Identification

KW - Spectral decomposition

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JO - Journal of Econometrics

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Spectral methods for identifying scalar diffusions

Abstract

Keywords

ASJC Scopus subject areas

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