Spectral methods for identifying scalar diffusions

Lars Peter Hansen, José Alexandre Scheinkman, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)1-32
Number of pages32
JournalJournal of Econometrics
Issue number1
StatePublished - Jun 15 1998


  • Continuous-time models in finance
  • Diffusion
  • Embeddability
  • Identification
  • Spectral decomposition

ASJC Scopus subject areas

  • Applied Mathematics
  • Economics and Econometrics


Dive into the research topics of 'Spectral methods for identifying scalar diffusions'. Together they form a unique fingerprint.

Cite this