The class of locally stationary processes assumes that there is a time-varying spectral representation, that is, the existence of finite second moment. We propose the α-stable locally stationary process by modifying the innovations into stable distributions and the indirect inference to estimate this type of model. Due to the infinite variance, some of interesting properties such as time-varying autocorrelation cannot be defined. However, since the α-stable family of distributions is closed under linear combination which includes the possibility of handling asymmetry and thicker tails, the proposed model has the same tail behaviour throughout the time. In this paper, we propose this new model, present theoretical properties of the process and carry out simulations related to the indirect inference in order to estimate the parametric form of the model. Finally, an empirical application is illustrated.

中文翻译：

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具有稳定创新的局部平稳 ARMA 过程的间接推理

局部平稳过程类假设存在时变谱表示，即有限二阶矩的存在。我们通过将创新修改为稳定分布和间接推断来估计这种类型的模型，从而提出了 α-stable 局部平稳过程。由于无穷大的方差，一些有趣的特性如时变自相关无法定义。然而，由于 α 稳定分布族在线性组合下是封闭的，其中包括处理不对称和较厚尾部的可能性，因此所提出的模型在整个时间内具有相同的尾部行为。在本文中，我们提出了这个新模型，介绍过程的理论特性并进行与间接推理相关的模拟，以估计模型的参数形式。最后，说明了一个经验应用。