ESTIMATION OF DIFFERENTIAL-DIFFERENCE EQUATION SYSTEMS WITH UNKNOWN LAG PARAMETERS
研究了滞后参数未知且不限于整数的随机微分差分方程系统的参数估计，提出了频域极大似然估计方法并证明了其渐近性质。
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.We are grateful to Gordon Kemp, Andrew Harvey, the Editor, and two anonymous referees for helpful comments on an earlier version of this paper. Any remaining errors are the sole responsibility of the authors. The first author thanks the Economic and Social Research Council for financial support under grant number R00429434216, and the second author thanks the Leverhulme Trust for financial support in the form of a Philip Leverhulme Prize.