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This paper evaluates the out-of-sample forecasting accuracy of seven models for weekly volatility in fourteen stock markets. Volatility is defined as within-week standard deviation of continuously compounded daily returns on the stock market index of each country for the period December 1987 to December 1997. Total volatility series include 522 weeks. The first half of the sample (261 weeks) is retained for the estimation of parameters while the second half is for the forecast period. The following models are employed: a random walk model, a historical mean model, moving average models, weighted moving average models, exponentially weighted moving average models, an exponential smoothing model, and a regression model. We first use the standard loss functions to evaluate the performance of the competing models: the mean error, the mean absolute error, the root mean squared error, and the mean absolute percentage error. We also employ the asymmetric loss functions to penalise under/over-prediction.

This paper evaluates the out-of-sample forecasting accuracy of eleven models for monthly volatility in fifteen stock markets. Volatility is defined as within-month standard deviation of continuously compounded daily returns on the stock market index of each country for the ten-year period 1988 to 1997. The first half of the sample is retained for the estimation of parameters while the second half is for the forecast period. The following models are employed: a random walk model, a historical mean model, moving average models, weighted moving average models, exponentially weighted moving average models, an exponential smoothing model, a regression model, an ARCH model, a GARCH model, a GJR-GARCH model, and an EGARCH model. First, standard (symmetric) loss functions are used to evaluate the performance of the competing models: mean absolute error, root mean squared error, and mean absolute percentage error. According to all of these standard loss functions, the exponential smoothing model provides superior forecasts of volatility. On the other hand, ARCH-based models generally prove to be the worst forecasting models. Asymmetric loss functions are employed to penalize under-/over-prediction. When under-predictions are penalized more heavily, ARCH-type models provide the best forecasts while the random walk is worst. However, when over-predictions of volatility are penalized more heavily, the exponential smoothing model performs best while the ARCH-type models are now universally found to be inferior forecasters.Stock market volatility, forecasting, forecast evaluation,

The changes in the volatility and liquidity of French stocks are examined before and after their cross-listing on the German electronic market, the Xetra. The results are mixed in terms of the change in liquidity and volatility of stocks after cross-listing. It is found that for many stocks volatility of stock prices increases and liquidity declines after cross-listing. Furthermore, similar results are obtained when market volatility in the Paris Bourse is controlled for. These results suggest the migration of orders to the Xetra and the deterioration of the quality of the Paris Bourse with the cross listing of French stocks on the German market, especially for those stocks that are continuously traded on the Xetra. These results seem to be against the integration of the French and German markets during the period analysed in this study. Furthermore, the findings indicate that the trading scheme and the characteristics of the stock should be considered in examining the cross-listing effects.

This is a pioneering effort to test in 14 countries the relationship between stock market returns and their forecast volatility derived from the symmetric and asymmetric conditional heteroscedasticity models. Both weekly and monthly returns and their volatility are investigated. An out-of-sample testing methodology is employed using volatility forecasts instead of investigating the relation between stock returns and their in-sample volatility estimates. Expected volatility is derived from the ARCH(p), GARCH(1,1), GJR-GARCH(1,1) and EGARCH(1,1) forecast models. Expected volatility is found to have a significant negative or positive effect on country returns in a few cases. Unexpected volatility has a negative effect on weekly stock returns in six to seven countries and on monthly returns in nine to eleven countries depending on the volatility forecasting model. However, it has a positive effect on weekly and monthly returns in none of the countries investigated. It is concluded that the return variance may not be an appropriate measure of risk.