The relatively exceptional performance of the mean-reverting model can also be seen from the results in Table 2 which reports the mean square prediction error of a given model relative to the MSPE of the GARCH(1,1).
For example, with one-month futures, and compared to the 5-year horizon, the three-year MSPE is 15 per cent smaller and the one-year MSPE is 33 per cent more accurate.
Using weekly and monthly frequencies, and for three forecast horizons, we examine the forecasts from the various models based on the mean square prediction error (MSPE) criterion.
Clearly, if the oil-sensitive stock price has a lower MSPE than the no-change forecast, the MSPE ratio will be less than 1.
In addition to examining the MSPE ratio, we also consider the directional accuracy of the forecasts, as measured by the success (hit) ratio indicating the relative frequency with which the predictive regression model based on the oil-sensitive stock price is able to predict correctly the sign of the change in the oil price.
Tables 6 and 7 show that for the 1-month forecast horizon (h = 1), the MSCI world energy sector indices and the MSCI marine index outperform the no-change forecast with statistical significance in terms of the MSPE criterion and the forecasting performance of the directional change in the price of oil.
The VAR and the ST-AR models yield lower MSPEs for almost every horizon.
This negates, to some extent, the reduction in the MSPEs gained by reducing parameter uncertainty in the more parsimoniously parameterized ST-AR model.
For example, most states yield lower MSPEs for the disaggregate forecasting models versus the aggregate AR model.
The means of the AIC, SBC, and MSPE for each of the models are reported in Table 1 for various values of [[alpha].sub.0], [[alpha].sub.1], and [[alpha].sub.2].
The situation is quite different when we consider the MSPE. As shown in the values for the MSPE of Table 1, the average value of the MSPE is always lowest for the true AR(2) model.
The means of the AIC, SBC, and MSPE for each type of model are reported in Table 2 and the distributions of the AIC, SBC, and MSPE for parameter set 4 are shown in Figures 5-7.