Methods for Computing Numerical Standard Errors: Review and Application to Value-at-Risk Estimation

Numerical standard error (NSE) is an estimate of the standard deviation of a simulation result if the simulation experiment were to be repeated many times. We review standard methods for computing NSE, and perform a Monte Carlo experiments to compare their performance in the case of high/extreme autocorrelation. In particular, we propose an application to risk management where we assess the precision of the Value–at–Risk measure when the underlying risk model is estimated by simulation–based methods. Overall, HAC estimators with prewhitening perform best in the presence of large/extreme autocorrelation.

Keywords: Bootstrap, GARCH, HAC kernel, numerical standard error (NSE), Monte Carlo, Markov chain Monte Carlo (MCMC), spectral density, Value-at-Risk precision

JEL Classification: C12, C15, C22

Suggested Citation: Suggested Citation

Ardia, David and Bluteau, Keven and Hoogerheide, Lennart F., Methods for Computing Numerical Standard Errors: Review and Application to Value-at-Risk Estimation (August 22, 2017). Journal of Time Series Econometrics, Vol. 10, No. 2, pp.1-9, 2018, Available at SSRN: https://ssrn.com/abstract=2741587 or http://dx.doi.org/10.2139/ssrn.2741587