Estimation of the value at risk (VaR) requires prediction of the future volatility. Whereas this is a simple task in ARCH and related models, it becomes much more complicated in stochastic volatility (SV) processes where the volatility is a function of a latent variable that is not observable. In-sample (present and past values) and out-of-sample (future values) predictions of that unobservable variable are thus necessary. This paper proposes singular spectrum analysis (SSA), which is a fully nonparametric technique that can be used for both purposes. A combination of traditional forecasting techniques and SSA is also considered to estimate the VaR. Their performance is assessed in an extensive Monte Carlo and with an application to a daily series of S&P500 returns.

中文翻译：

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随机波动率模型中风险价值的奇异谱分析

风险价值 (VaR) 的估计需要预测未来的波动性。虽然这在 ARCH 和相关模型中是一项简单的任务，但在随机波动率 (SV) 过程中变得更加复杂，其中波动率是不可观察的潜在变量的函数。因此，必须对该不可观察变量进行样本内（当前值和过去值）和样本外（未来值）预测。本文提出了奇异谱分析 (SSA)，这是一种完全非参数化的技术，可用于这两种目的。传统预测技术和 SSA 的组合也被认为是估计 VaR。他们的表现在广泛的蒙特卡洛中进行评估，并应用于标准普尔 500 指数的每日系列回报。