试测稳定自动递减模型 (Tempered Stable Autoregressive Models)

In this article, we introduce and study a one sided tempered stable first order autoregressive model called TAR(1). Under the assumption of stationarity of the model, the marginal probability density function of the error term is found. It is shown that the distribution of the error term is infinitely divisible. Parameter estimation of the introduced TAR(1) process is done by adopting the conditional least square and method of moments based approach and the performance of the proposed methods are evaluated on simulated data. Also we study an autoregressive model of order one with tempered stable innovations. Using appropriate test statistic it is shown that the model fit very well on real and simulated data. Our models generalize the inverse Gaussian and one-sided stable autoregressive models existing in the literature.

翻译：在本篇文章中,我们引入并研究一个侧面有色稳定第一顺序的自动递减模型,称为TAR(1)。根据模型的固定性假设,发现错误术语的边际概率密度功能,显示错误术语的分布是无限的,错误术语的分布是无限的,对引入的TAR(1)过程的参数估计是通过采用条件最小的平方法和以瞬间为基础的方法进行的,对拟议方法的性能进行模拟数据评估。我们还研究一个具有温和稳定创新的自动递减型顺序模型。我们利用适当的测试统计数据,发现该模型非常适合真实和模拟数据。我们的各种模型概括了文献中存在的反高斯和单向稳定的自动递增模式。