Bootstrapping Time-Varying Uncertainty Intervals for Extreme Daily Return Periods

Katleho Makatjane and Tshepiso Tsoku
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Tshepiso Tsoku: Department of Statistics and Operations Research, North-West University, Mafikeng Campus, Mmabatho 2745, South Africa

IJFS, 2022, vol. 10, issue 1, 1-23

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.

Keywords: expected shortfall; generalized autoregressive score; extreme value theory; generalized extreme value distribution; stock returns; time-varying; Value-at-Risk (search for similar items in EconPapers)
JEL-codes: F2 F3 F41 F42 G1 G2 G3 (search for similar items in EconPapers)
Date: 2022
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