A COMPARISON BETWEEN LINEAR AND NONLINEAR FORECASTS FOR NONLINEAR AR MODELS

In this paper the relative forecast performance of nonlinear models to linear models is assessed by the conditional probability that the abs olute forecast error of the nonlinear forecast is smaller than that of the linear forecast. The comparison probability is explicitly express ed and is shown to be an increasing function of the distance between n onlinear and linear forecasts under certain conditions. This expressio n of the comparison probability may not only be useful in determining the predictor, which is either a more accurate or a simpler forecast, to be used but also provides a good explanation for an odd phenomenon discussed by Pemberton. The relative forecast performance of a nonline ar model to a linear model is demonstrated to be sensitive to its fore cast origins. A new forecast is thus proposed to improve the relative forecast performance of nonlinear models based on forecast origins. (C ) 1997 John Wiley & Sons, Ltd.