A simple estimator for discrete-time samples from affine stochastic delay differential equations
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Estimation for discrete time observations of an affine stochastic delay differential equation is considered. The delay measure is assumed to be concentrated on a finite set. A simple estimator is obtained by discretization of the continuous-time likelihood function, and its asymptotic properties are investigated. The estimator is very easy to calculate and works well at high sampling frequencies, but it is shown to have a significant bias when the sampling frequency is low.
KeywordsAsymptotic normality Discrete time observation of continuous time models Stochastic delay differential equation
Mathematics Subject Classification (2000)62M09 34K50
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- Bradley RC (2007) Introduction to strong mixing conditions. Kendrick Press, Heber City, UTGoogle Scholar
- Doukhan P (1994) Mixing, properties and examples. Springer, New York. Lecture Notes in Statistics 85Google Scholar
- Gushchin AA, Küchler U (2003) On parametric statistical models for stationary solutions of affine stochastic delay differential equations. Math Methods Stat 12: 31–61Google Scholar
- Küchler U, Sørensen M (2009) Statistical inference for discrete-time samples from affine stochastic delay differential equations. Preprint, Department of Mathematical Sciences, University of Copenhagen.Google Scholar
- Reiß M (2002b) Nonparametric estimation for stochastic delay differential equations. PhD thesis, Institut für Mathematik, Humboldt-Universität zu BerlinGoogle Scholar