The approximation expression about error accumulation of a long-term prediction is derived. By analyzing this formula, we find that the factors that can affect the long-term predictability include the model parameters, prediction errors and the derivates of the used basis functions. To enlarge the maximum attempting time, we present that more suitable basis functions should be those with smaller derivative functions and a fast attenuation where out of the time series range. We compare the long-term predictability of a non-polynomial based algorithm and a polynomial one to prove the success of our method.