论文标题
具有有限第二矩的固定状态空间模型的质量估计
Whittle estimation for stationary state space models with finite second moments
论文作者
论文摘要
在本文中，我们考虑了以低频采样的连续时间线性空间模型的固定解的参数。在我们的上下文中，驾驶过程是一个lévy过程，它允许基础模型的灵活边距。莱维过程应该有有限的第二时刻。众所周知，当时线性状态空间模型的固定解决方案和多元CARMA过程的类别重合。我们证明，基于周期图的晶状估计器是强烈一致的，并且在渐近地正态分布。与离散时间ARMA模型的经典设置的比较表明，在连续设置Whittle估计器的极限协方差矩阵中，非高斯模型具有额外的校正项。为了证明，我们还研究了综合期刊的渐近正态性，这本身很有趣。它可用于构建拟合测试的优点。此外，对于Carma过程的单变量状态空间过程，我们引入了Whittle估计器的调整后版本，并得出了该估计量的渐近性能。通过模拟研究证明了我们的估计器的实际适用性。
In this paper, we consider the Whittle estimator 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. It is well known that then the class of stationary solutions of linear state space models and the class of multivariate CARMA processes coincides. We prove that the Whittle estimator, which is based on the periodogram, is strongly consistent and asymptotically normally distributed. A comparison with the classical setting of discrete-time ARMA models shows that in the continuous-time setting the limit covariance matrix of the Whittle estimator has an additional correction term for non-Gaussian models. For the proof, we investigate as well the asymptotic normality of the integrated periodogram which is interesting for its own. It can be used to construct goodness of fit tests. Furthermore, for univariate state space processes, which are CARMA processes, we introduce an adjusted version of the Whittle estimator and derive as well the asymptotic properties of this estimator. The practical applicability of our estimators is demonstrated through a simulation study.
