论文标题
估计$α$稳定的Carma处理的注释，以低频采样
A note on estimation of $α$-stable CARMA processes sampled at low frequencies
论文作者
论文摘要
在本文中，我们调查了对称$α$稳定的Carma工艺的估计器。仿真研究表明，GARC \'ıa等人中介绍的值估计器和估计量。 （2011年）是稳定CARMA过程参数的一致估计器。对于有限第二矩的Carma过程，众所周知，晶状估计器是一致的，并且在渐近地正态分布。因此，在轻尾设置CARMA工艺中的Whittle估计器的性质与ARMA过程的Whittle估计量相似。但是，在本文中，我们证明，通常，在低频下采样的对称$α$稳定的Carma工艺的Whittle估计量并不一致，并突出了为什么模拟研究建议其他建议。因此，与灯塔设定的重型ARMA工艺的晶体估计器的性质相反，不能将其转移到重尾Carma工艺上。我们也阐述了Garc \'ıa等人中提出的估计器。 （2011）面临同样的问题。但是，稳定的汽车（1）过程的小估计器是一致的。
In this paper, we investigate estimators for symmetric $α$-stable CARMA processes sampled equidistantly. Simulation studies suggest that the Whittle estimator and the estimator presented in Garc\'ıa et al. (2011) are consistent estimators for the parameters of stable CARMA processes. For CARMA processes with finite second moments it is well-known that the Whittle estimator is consistent and asymptotically normally distributed. Therefore, in the light-tailed setting the properties of the Whittle estimator for CARMA processes are similar to those of the Whittle estimator for ARMA processes. However, in the present paper we prove that, in general, the Whittle estimator for symmetric $α$-stable CARMA processes sampled at low frequencies is not consistent and highlight why simulation studies suggest something else. Thus, in contrast to the light-tailed setting the properties of the Whittle estimator for heavy-tailed ARMA processes can not be transferred to heavy-tailed CARMA processes. We elaborate as well that the estimator presented in Garc\'ıa et al. (2011) faces the same problems. However, the Whittle estimator for stable CAR(1) processes is consistent.
