论文标题
固定状态空间模型的经验光谱过程
Empirical spectral processes for stationary state space models
论文作者
论文摘要
在本文中，我们考虑了函数指数的归一化加权期间图，用于等距采样的多元连续时间状态空间模型，这些模型是多元连续时间ARMA过程。因此，采样距离是固定的，驾驶Lévy工艺至少具有有限的第四刻。在对功能空间和驱动lévy过程的矩时的不同假设下，我们得出了函数指数归一化加权集成期刊的中心限制定理。对功能空间的假设或对莱维过程矩的存在的假设要么较弱。此外，我们在连续函数的空间和双重空间中均显示了弱收敛性，并显示了高斯过程，并给出了协方差函数的明确表示。该结果可用于得出Whittle估计器的渐近行为，并构建拟合优度测试统计量作为Grenander-Rosenblatt统计量和Cramér-von Mises统计量。我们介绍了统计数据的确切极限分布，并通过模拟研究显示其性能。
In this paper, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling distance is fixed and the driving Lévy process has at least a finite fourth moment. Under different assumptions on the function space and the moments of the driving Lévy process we derive a central limit theorem for the function-indexed normalized weighted integrated periodogram. Either the assumption on the function space or the assumption on the existence of moments of the Lévy process is weaker. Furthermore, we show the weak convergence in both the space of continuous functions and in the dual space to a Gaussian process and give an explicit representation of the covariance function. The results can be used to derive the asymptotic behavior of the Whittle estimator and to construct goodness-of-fit test statistics as the Grenander-Rosenblatt statistic and the Cramér-von Mises statistic. We present the exact limit distributions of both statistics and show their performance through a simulation study.
