We consider Whittle estimation for the parameters of a stationary solution of a continuous-time linear state space model sampled at low frequencies. In our context, the driving process is a Lévy process which allows flexible margins of the underlying model. The Lévy process is supposed to have finite second moments. Then, the classes of stationary solutions of linear state space models and of multivariate CARMA processes coincide. We prove that the Whittle estimator, which is based on the periodogram, is strongly consistent and asymptotically normal. A comparison with ARMA models shows that in the continuous-time setting the limit covariance matrix of the estimator has an additional term for non-Gaussian models. Thereby, we investigate the asymptotic normality of the integrated periodogram. Furthermore, for univariate processes we introduce an adjusted version of the Whittle estimator and derive its asymptotic properties. The practical applicability of our estimators is demonstrated through a simulation study.

我们考虑对低频采样的连续时间线性状态空间模型的平稳解的参数进行 Whittle 估计。在我们的上下文中，驱动过程是一个 Lévy 过程，它允许底层模型的灵活边距。Lévy 过程应该具有有限的二阶矩。然后，线性状态空间模型和多元 CARMA 过程的平稳解的类别重合。我们证明了基于周期图的 Whittle 估计量是强一致且渐近正态的。与 ARMA 模型的比较表明，在连续时间设置中，估计器的极限协方差矩阵有一个非高斯模型的附加项。因此，我们研究了积分周期图的渐近正态性。此外，对于单变量过程，我们引入了 Whittle 估计量的调整版本并推导出其渐近特性。我们的估算器的实际适用性通过模拟研究得到证明。