Singular spectrum analysis for value at risk in stochastic volatility models

Abstract

AbstractEstimation 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.