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April 2005 Diffusion-type models with given marginal distribution and autocorrelation function
Bo Martin Bibby, Ib Michael Skovgaard, Michael Sørensen
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Bernoulli 11(2): 191-220 (April 2005). DOI: 10.3150/bj/1116340291


Flexible stationary diffusion-type models are developed that can fit both the marginal distribution and the correlation structure found in many time series from, for example, finance and turbulence. Diffusion models with linear drift and a known and prespecified marginal distribution are studied, and the diffusion coefficients corresponding to a large number of common probability distributions are found explicitly. An approximation to the diffusion coefficient based on saddlepoint techniques is developed for use in cases where there is no explicit expression for the diffusion coefficient. It is demonstrated theoretically as well as in a study of turbulence data that sums of diffusions with linear drift can fit complex correlation structures. Any infinitely divisible distribution satisfying a weak regularity condition can be obtained as a marginal distribution.


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Bo Martin Bibby. Ib Michael Skovgaard. Michael Sørensen. "Diffusion-type models with given marginal distribution and autocorrelation function." Bernoulli 11 (2) 191 - 220, April 2005.


Published: April 2005
First available in Project Euclid: 17 May 2005

zbMATH: 1066.60071
MathSciNet: MR2132002
Digital Object Identifier: 10.3150/bj/1116340291

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability


Vol.11 • No. 2 • April 2005
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