Bootstrapping Time-Varying Uncertainty Intervals for Extreme Daily Return Periods

Abstract

This study aims to overcome the problem of dimensionality, accurate estimation, and forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) uncertainty intervals in high frequency data. A Bayesian bootstrapping and backtest density forecasts, which are based on a weighted threshold and quantile of a continuously ranked probability score, are developed. Developed backtesting procedures revealed that an estimated Seasonal autoregressive integrated moving average-generalized autoregressive score-generalized extreme value distribution (SARIMA–GAS–GEVD) with a skewed student-t distribution had the best prediction performance in forecasting and bootstrapping VaR and ES. Extension of this non-stationary distribution in literature is quite complicated since it requires specifications not only on how the usual Bayesian parameters change over time but also those with bulk distribution components. This implies that the combination of a stochastic econometric model with extreme value theory (EVT) procedures provides a robust basis necessary for the statistical backtesting and bootstrapping density predictions for VaR and ES.

Towards Financing System of Integrated Enterprise Development in the Time of COVID-19 Outbreak

“…Earlier researches have taken similar approaches to model formation, but compared to this study have a fragmented approach. For instance, there are results that concentrate on the mathematical component of a stochastic econometric model with extreme value theory procedures, which provides the sound basis needed for statistical testing on historical data and initial density forecasts (Makatjane and Tsoku 2022). Alternatively, the approach is based entirely on the micro-level as a starting point for determining the equilibrium mechanism of the economy (Trinh 2022).…”