Reduce forecasting errors by low order nonlinear transformations for complex time series

Besides the forecasting errors by a model with not entirely describing the characteristics of the complex systems in the real world, a digital computer can produce additive errors due to its finite digits, such as the singularity in matrix inversion, if there are large white noise in the forecasted series. Low order nonlinear transformations can make the inputted data of forecasting models to an appropriate signal to noise ratio, decrease the bad influence of the "trend", and make a high order forecasting model equivalently into a linear model, even a lower order model than a linear one. All these advantages reduce the forecasting errors. The numerical experiments support the theoretical analyses of a low order nonlinear transformation.