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This study introduces the radial basis function neural network predictor (RBFP) to compare with regression, cumulative 3 points least squared linear model, grey prediction model GM(1,1|a), Box-Jenkins, and Holt-Winters smoothing utilized for the applications of non-periodic short-term time series forecast. Statistics methods and GM(1,1|a) predictor have been widely applicable on the issue of short-term forecasting for years. However, methods out of statistics encounter the crucial problem that the predicted values always cannot achieve the satisfactory results because the generalization capability of those traditional models can perform extrapolation well, especially in the domain of nonperiodic short-term forecast. Even though the GM(1,1|a) model performs well in many complicated systems, it still has trouble with a big singleton residual error being frequently occurring at the position around the turning points region, that is, an overshooting effect. Furthermore, the cumulative 3 points least mean squared linear model possibly generates an underestimated output. Therefore, this study proposes a radial based function predictor (RBFP) to improve generalization capability for extrapolation. The verification of this study also experiments successfully in the stock price index forecast, and the results of RBFP have achieved the best accuracy on the predicted stock price indexes as compared with the others.