A comparison between linear and nonlinear forecasts for nonlinear autoregressive models

In this paper the relative forecast performance of nonlinear models to linear models is assessed by the conditional probability that the absolute forecast error of the nonlinear forecast is smaller than that of the linear forecast. The comparison probability is explicitly expressed and is shown to be an increasing function of the distance between nonlinear and linear forecasts under certain conditions. This expression of the comparison probability may not only be useful in determining the predictor, which is either a more accurate or a simple forecast, to be used but also provides a good explanation for an odd phenomenon discussed by Pemberton. The relative forecast performance of a nonlinear model to a linear model is demonstrated to be sensitive to its forecast origins. A new forecast is thus proposed to improve the relative forecast performance of nonlinear models based on forecast origins.