On the use of power transformations in CAViaR models

Value at risk (VaR) is a risk measure widely used by financial institutions in allocating risk. VaR forecast estimation involves the conditional evaluation of quantiles based on the currently available information. Recent advances in VaR evaluation incorporate a proxy for conditional variance, yielding the conditional autoregressive VaR (CAViaR) models. However, early work in finance literature has shown that the introduction of power transformations has resulted in improvements in volatility forecasting. Having a direct association between volatility and conditional VaR, we adopt power-transformed CAViaR models. We investigate whether the flexible conditional VaR dynamics associated with power-transformed CAViaR models can result in better forecasting results than those assumed by the nontransformed CAViaR models. Estimation in CAViaR models is based on an early-rejection Markov chain Monte Carlo algorithm. We illustrate our forecasting evaluation results using simulated and financial daily return data series. The results demonstrate that there is strong evidence that supports the use of power-transformed CAViaR models when forecasting VaR.