Improved Duration-Based Backtesting of Value-at-Risk

Backtesting value-at-risk forecasts is an important issue. A duration-based approach has recently been proposed by Christoffersen and Pelletier (2004). Their method is very appealing because it allows one to test for both correct conditional and unconditional coverage against quite general alternatives, thus generalizing earlier approaches. Despite the discrete nature of the problem, the authors used the continuous Weibull distribution in their implementation of the method. In this paper, we employ the discrete counterpart of this model instead. We argue that the discrete approach has two advantages. First, the parameters involved have a clear-cut interpretation in risk management terms. Moreover, and more importantly, simulations indicate that the discrete model has superior power properties to the continuous candidate. As the discrete Weibull distribution is not well known in the risk management literature, its properties relevant to backtesting are also briefly discussed