A comparison of bootstrap and Monte-Carlo testing approaches to value-at-risk diagnosis

• Published in: Computational statistics Vol. 25; no. 4; pp. 725 - 732
• Main Authors: Herwartz, Helmut, Waichman, Israel
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.12.2010; Springer Nature B.V
• Subjects: Approximation; Asymptotic properties; Bootstrap method; Computer simulation; Convergence; Dependent variables; Economic Theory/Quantitative Economics/Mathematical Methods; Hypotheses; Likelihood ratio; Mathematical models; Mathematics and Statistics; Monte Carlo methods; Monte Carlo simulation; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Random variables; Regression analysis; Resampling; Short Note; Simulation; Statistics; Studies; Variables; Bootstrap; Monte Carlo test; Dynamic quantile test; Value-at-risk
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-010-0194-4

In this note we investigate a particular resampling scheme and Monte Carlo testing to determine critical values for two test statistics typically used for diagnosing value-at-risk models. In cases of small nominal coverage subjected to testing, the dynamic quantile test and a corresponding logit based likelihood ratio test suffer from poor convergence to the asymptotic limit distribution. In terms of empirical size both resampling and Monte Carlo approaches offer most accurate test features with the Monte Carlo technique achieving power gains if a misspecified value-at-risk model is subjected to testing.