Forecasting (Log) Volatility Models

Paper number: 98/14

Paper date: 1 December 1998

Year: 1998

Paper Category: Discussion Paper


George A Christodoulakis*, **


Stephen E Satchell**, ***


A number of volatility forecasting studies has led to the perception that the ARCH- and Stochastic Volatility-type models provide poor out-of-sample forecasts of volatility. This is primarily based on the use of traditional forecast evaluation criteria concerning the accuracy and the unbiasedness of forecasts.

In this paper we provide an assessment of volatility forecasting. We use the Log- Volatility framework to show how the inherent noise in the approximation of the actual- and unobservable- volatility by the squared return results in a misleading forecast evaluation. We characterise this noise and explicitly quantify its effects assuming normal errors. We extend our results using more general error structures such as the Compound Normal and the Gram-Charlier classes of distributions. We argue that evaluation problems are likely to be exacerbated by non-normality of the shocks and that non-linear and utility-based criteria can be more suitable for the evaluation of volatility forecasts.

JEL Classification Nos: G00; C53; C52; C15
Keywords: Compound Normal, EGARCH, expected utility; forecasting; Gram-Charlier; mean squared error; non normality; Stochastic volatility.

Corresponding Author: George A Christodoulakis, Department of Economics, University of Exeter, Streatham Court, Rennes Drive, Exeter, EX4 4PU, UK, tel: (44) 1392 263212, fax (44) 1392 263242, email: G. Christodoulakis


* University of Exeter
** Brikbeck College, University of London
*** Faculty of Economics and Trinity College, University of Cambridge