通过ARMA表示的log-GARCH模型

Genaro Sucarrat
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引用次数: 4

摘要

log-GARCH模型为经济不确定性、金融波动性和其他正值变量的建模提供了一个灵活的框架。它的指数规范确保拟合的波动性是正的,允许灵活的动力学,简化了在null下参数等于零时的推理,并且对数变换使模型对跳跃或异常值具有鲁棒性。另一个优点是该模型允许类似arma的表示。这意味着log-GARCH模型可以很容易地通过广泛使用的软件进行估计,并使广泛的众所周知的时间序列结果和方法成为可能。本章概述了log-GARCH模型及其ARMA表示,以及如何在实践中实现估计。在介绍之后,我们描述了具有波动性不对称(“杠杆”)的单变量log-GARCH模型,并展示了如何获得其(非线性)ARMA表示。接下来,加入平稳协变量(“X”),然后用经验说明不对称的一阶规范。然后我们将注意力转向多元log-GARCH-X模型。我们首先以其一般形式呈现多元规范,但很快将我们的重点转向可以逐个方程估计的规范-甚至在未知形式的动态条件关联(dcc)存在的情况下。其次,建立了多元非平稳log-GARCH-X模型,其中x协变量既可以是平稳的,也可以是非平稳的。针对log-GARCH模型的一个常见批评是,它的ARCH项可能不存在于内线中。有一节专门讨论如何在实践中处理这一问题。其次,将log-GARCH模型推广到对数乘法误差模型(MEMs)。最后,本章结束。JEL分类:C22, C32, C51, C58
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The log-GARCH model via ARMA representations
The log-GARCH model provides a flexible framework for the modelling of economic uncertainty, financial volatility and other positively valued variables. Its exponential specification ensures fitted volatilities are positive, allows for flexible dynamics, simplifies inference when parameters are equal to zero under the null, and the logtransform makes the model robust to jumps or outliers. An additional advantage is that the model admits ARMA-like representations. This means log-GARCH models can readily be estimated by means of widely available software, and enables a vast range of well-known time-series results and methods. This chapter provides an overview of the log-GARCH model and its ARMA representation(s), and of how estimation can be implemented in practice. After the introduction, we delineate the univariate log-GARCH model with volatility asymmetry (“leverage”), and show how its (nonlinear) ARMA representation is obtained. Next, stationary covariates (“X”) are added, before a first-order specification with asymmetry is illustrated empirically. Then we turn our attention to multivariate log-GARCH-X models. We start by presenting the multivariate specification in its general form, but quickly turn our focus to specifications that can be estimated equation-by-equation – even in the presence of Dynamic Conditional Correlations (DCCs) of unknown form. Next, a multivariate non-stationary log-GARCH-X model is formulated, in which the X-covariates can be both stationary and/or nonstationary. A common critique directed towards the log-GARCH model is that its ARCH terms may not exist in the presence of inliers. An own Section is devoted to how this can be handled in practice. Next, the generalisation of log-GARCH models to logarithmic Multiplicative Error Models (MEMs) is made explicit. Finally, the chapter concludes. JEL Classification: C22, C32, C51, C58
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