Optimal multi-step-ahead prediction of ARCH/GARCH models and NoVaS transformation

This paper gives a computer-intensive approach to multi-step-ahead prediction of volatility in financial returns series under an ARCH/GARCH model and also under a model-free setting, namely employing the NoVaS transformation. Our model-based approach only assumes i..id innovations without requiring knowledge/assumption of the error distribution and is computationally straightforward. The model-free approach is formally quite similar, albeit a GARCH model is not assumed. We conducted a number of simulations to show that the proposed approach works well for both point prediction (under L1 and/or L2 measures) and prediction intervals that were constructed using bootstrapping. The performance of GARCH models and the model-free approach for multi-step ahead prediction was also compared under different data generating processes.