Least-squares estimation of GARCH(1,1) models with heavy-tailed errors

IF 2.9 4区 经济学 Q1 ECONOMICS
Arie Preminger, Giuseppe Storti
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引用次数: 5

Abstract

GARCH(1,1) models are widely used for modelling processes with time-varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a novel log-transform-based least-squares approach to the estimation of GARCH(1,1) models. Within this approach, the scale of the estimated volatility is dependent on an unknown tuning constant. By means of a backtesting exercise on both real and simulated data, we show that knowledge of the tuning constant is not crucial for Value at Risk prediction. However, this does not apply to many other applications where correct identification of the volatility scale is required. In order to overcome this difficulty, we propose two alternative two-stage least-squares estimators and we derive their asymptotic properties under very mild moment conditions for the errors. In particular, we establish the consistency and asymptotic normality at the standard convergence rate of for our estimators. Their finite sample properties are assessed by means of an extensive simulation study.

具有重尾误差的GARCH(1,1)模型的最小二乘估计
GARCH(1,1)模型广泛用于具有时变波动率的过程的建模。这包括金融时间序列,它可能特别重尾。在本文中,我们提出了一种新的基于对数变换的最小二乘方法来估计GARCH(1,1)模型。在这种方法中,估计波动的规模依赖于一个未知的调整常数。通过对真实和模拟数据的回测练习,我们表明,调整常数的知识对于风险值预测并不重要。然而,这并不适用于许多其他需要正确识别波动性的应用。为了克服这一困难,我们提出了两个可选的两阶段最小二乘估计,并推导了它们在非常温和的矩条件下的渐近性质。特别地,我们建立了估计量在标准收敛速率下的相合性和渐近正态性。通过广泛的模拟研究评估了它们的有限样本性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Econometrics Journal
Econometrics Journal 管理科学-数学跨学科应用
CiteScore
4.20
自引率
5.30%
发文量
25
审稿时长
>12 weeks
期刊介绍: The Econometrics Journal was established in 1998 by the Royal Economic Society with the aim of creating a top international field journal for the publication of econometric research with a standard of intellectual rigour and academic standing similar to those of the pre-existing top field journals in econometrics. The Econometrics Journal is committed to publishing first-class papers in macro-, micro- and financial econometrics. It is a general journal for econometric research open to all areas of econometrics, whether applied, computational, methodological or theoretical contributions.
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