Model-free versus Model-based Volatility Prediction

Abstract

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. 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.