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ABSTRACT
Recent research has suggested that forecast evaluation on the basis of standard statistical loss functions could prefer models which are sub-optimal when used in a practical setting. This paper explores a number of statistical models for predicting the daily volatility of several key UK financial time series. The out-of-sample forecasting performance of various lineal' and GARCH-type models of volatility are compared with forecasts derived from a multivariate approach. The forecasts are evaluated using traditional metrics, such as mean squared error, and also by how adequately they perform in a modern risk management setting. We find that the relative accuracies of the various methods are highly sensitive to the measure used to evaluate them. Such results have implications for any econometric time series forecasts which are subsequently employed in financial decision making. Copyright © 2003 John Wiley & Sons, Ltd.
KEY WORDS internal risk management models; asset return volatility; Value at Risk models; forecasting; univariate and multivariate GARCH models
(ProQuest Information and Learning: ... denotes formulae omitted.)
INTRODUCTION
Modelling and forecasting stock market volatility has been the subject of a great deal of debate over the past fifteen years or so. Volatility, usually measured by the standard deviation of portfolio returns, is uniquely important in financial markets, for it is often taken to represent the portfolio's risk. Consequently, the literature on forecasting volatility is sizeable and still growing. Akgiray (1989), for example, finds the GARCH model superior to ARCH, exponentially weighted moving average, and historical mean models for forecasting monthly US stock index volatility. A similar result concerning the apparent superiority of GARCH is observed by West and Cho (1995) using onestep-ahead forecasts of dollar exchange rate volatility, evaluated using root-mean squared prediction errors. However, for longer horizons, the model behaves no better than their alternatives.1 Also using the same models and data, West et al. (1993) use asymmetric, utility-based criteria for evaluating the conditional variance forecasts, finding that GARCH models tend to yield the highest utilities. Pagan and Schwert (1990) compare GARCH, EGARCH, Markov switching regime and three nonparametric models for forecasting monthly US stock return volatilities. The EGARCH followed by the GARCH models perform moderately; the remaining models produce very poor predictions. Franses and van Dijk (1996) compare three members of the...