Abstract

In this article, we propose a nonparametric approach to estimating generalized autoregressive conditional heteroskedasticity (1,1) models with time-varying parameters. We model the time-varying parameters as a smooth function of time and estimate them using a local linear estimator. We show that our estimator is consistent and is asymptotically normal and that the proposed estimator outperforms a rolling window estimator in Monte Carlo simulation experiments. We present strong evidence of parameter instabilities using daily returns of stock indices and explore implications to risk management measures, such as value-at-risk and expected shortfall, through backtesting.

中文翻译：

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时变参数GARCH模型的局部线性估计和相关的风险测度

摘要

在本文中，我们提出了一种非参数方法来估计具有时变参数的广义自回归条件异方差（1,1）模型。我们将时变参数建模为时间的平滑函数，并使用局部线性估计器对其进行估计。我们证明了我们的估计量是一致的，并且是渐近正态的，并且在蒙特卡洛模拟实验中，所提出的估计量优于滚动窗口估计量。我们使用股指的日收益率来提供参数不稳定性的有力证据，并通过回测来探索对风险管理措施的影响，例如风险价值和预期的短缺。