Asymptotic normality
consistency
discrete time observation of continuous time models
predictionbased estimating functions
pseudolikelihood
stochastic delay differential equation
quasilikelihood.
Statistical inference for discretetime samples from affine stochastic delay differential equations.
Uwe Küchler
Küchler
Uwe
Michael Sørensen
Sørensen
Michael
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976), 25
Uwe Küchler
,
Michael Sørensen
Preprint series:
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976), 25
MSC 2000
 62M09 NonMarkovian processes: estimation

34K50 Stochastic delay equations
Abstract
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudolikelihood estimators, which are easy to calculate in practice. Also a more general class of predictionbased estimating functions is investigated. In particular, the optimal predictionbased estimating function and the asymptotic properties of the estimators are derived. The maximum pseudolikelihood estimator is a particular case, and an expression is found for the efficiency loss when using the maximum pseudolikelihood estimator rather than the computationally more involved optimal predictionbased estimator. The distribution of the pseudolikelihood estimator is investigated in a simulation study. For models where the delay measure is concentrated on a finite set, an estimator obtained by discretization of the continuoustime likelihood function is presented, and its asymptotic properties are investigated. The estimator is very easy to calculate, but it is shown to have a significant bias when the sampling frequency is low. Two examples of affine stochastic delay equation are considered in detail.
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