Model-free versus Model-based Volatility Prediction

The well-known ARCH/GARCH models for financial time series have been criticized of late for their poor performance in volatility prediction, that is, prediction of squared returns.-super-1 Focusing on three representative data series, namely a foreign exchange series (Yen vs. Dollar), a stock index series (the S&P500 index), and a stock price series (IBM), the case is made that financial returns may not possess a finite fourth moment. Taking this into account, we show how and why ARCH/GARCH models—when properly applied and evaluated—actually do have nontrivial predictive validity for volatility. Furthermore, we show how a simple model-free variation on the ARCH theme can perform even better in that respect. The model-free approach is based on a novel normalizing and variance-stabilizing transformation (NoVaS, for short) that can be seen as an alternative to parametric modeling. Properties of this transformation are discussed, and practical algorithms for optimizing it are given. Copyright , Oxford University Press.