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Journal of Financial Econometrics Advance Access originally published online on March 8, 2007
Journal of Financial Econometrics 2007 5(3):358-359; doi:10.1093/jjfinec/nbm004
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Copyright © The Author 2007. Published by Oxford University Press.

Model-free versus Model-based Volatility Prediction

Dimitris N. Politis
     University of California at San Diego

Address correspondence to Dimitris N. Politis, Departments of Mathematics and Economics, University of California at San Diego, La Jolla, CA 92093-0112, or e-mail: dpolitis{at}ucsd.edu


  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.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.

KEYWORDS: ARCH/GARCH models, forecasting, L1 methods, volatility

This article was presented as a keynote address at the "International Workshop on Recent Advances in Time Series Analysis", Cyprus, June 2004, as well as the 2nd International Symposium "Advances in Financial Forecasting", October 2005, Loutraki, Greece. Many thanks are due to the participants for helpful feedback, and in particular to Professors E. Paparoditis and D. Thomakos. The support of the National Science Foundation through grants DMS-01-04059 and SES-04-18136 is also gratefully acknowledged.

Received November 11, 2005; revised December 11, 2006; accepted January 30, 2007


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