Bernoulli

  • Bernoulli
  • Volume 19, Number 2 (2013), 409-425.

Statistical inference for discrete-time samples from affine stochastic delay differential equations

Uwe Küchler and Michael Sørensen

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Abstract

Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class of prediction-based estimating functions is investigated as well. In particular, the optimal prediction-based estimating function and the asymptotic properties of the estimators are derived. The maximum pseudo-likelihood estimator is a particular case, and an expression is found for the efficiency loss when using the maximum pseudo-likelihood estimator, rather than the computationally more involved optimal prediction-based estimator. The distribution of the pseudo-likelihood estimator is investigated in a simulation study. Two examples of affine stochastic delay equation are considered in detail.

Article information

Source
Bernoulli, Volume 19, Number 2 (2013), 409-425.

Dates
First available in Project Euclid: 13 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1363192033

Digital Object Identifier
doi:10.3150/11-BEJ411

Mathematical Reviews number (MathSciNet)
MR3037159

Zentralblatt MATH identifier
06168758

Keywords
asymptotic normality composite likelihood consistency discrete time observation of continuous-time models prediction-based estimating functions pseudo-likelihood stochastic delay differential equation

Citation

Küchler, Uwe; Sørensen, Michael. Statistical inference for discrete-time samples from affine stochastic delay differential equations. Bernoulli 19 (2013), no. 2, 409--425. doi:10.3150/11-BEJ411. https://projecteuclid.org/euclid.bj/1363192033


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