Comparison of Some Chosen Tests of Independence of Value-at-Risk Violations

Abstract

Backtesting is the necessary statistical procedure to evaluate performance of Value-at-Risk models. A satisfactory test should allow to detect both deviations from the correct probability of violations, as well as their clustering. Many researchers and practitioners underline the importance of the lack of any dependence in the hit series over time. If the independence condition is not met, it may be a signal that the Value at Risk model reacts too slowly to changes in the market. If the violation sequence exhibits a dependence other than first order Markov dependence, the classical test of Christoffersen would fail to detect it. This article presents a test based on analysis of duration, having power against more general forms of dependence, based on the same set of information as the Christoffersen test, i.e. hit series.The aim of this article is to analyze presented backtests, focusing on the aspect of limited data sets and the power of tests. Simulated data representing asset returns are used here. This paper is a continuation of earlier research done by the author.