ESTIMATION OF DIFFERENTIAL-DIFFERENCE EQUATION SYSTEMS WITH UNKNOWN LAG PARAMETERS

This paper considers the estimation of the parameters of general systems of stochastic differential-difference equations in which the lag parameters themselves are treated as unknown and are not restricted to be integers and therefore form part of the parameter vector to be estimated. The asymptotic properties of an infeasible frequency domain maximum likelihood estimator are established in addition to those of a feasible version based on truncating an infinite series that arises in the computation of the spectral density function of the observed discrete time series. Precise conditions that the truncation parameter must satisfy for the asymptotic results to hold are provided. © 2006 Cambridge University Press.