Reducing forecast errors by logarithmic transformations for complex time series

Both nonlinear theories and Fourier analysis predicate theoretically that low-order nonlinear transformation has three advantages. First, it can increase the signal-to-noise ratio of a complex time series that has a large fluctuation. Second, it can insulate negative effects of outliers or bad data. Last, it can improve the distinction between the signal and white noise. The trend in the classical decomposition of “trend plus seasonals plus residuals” of a complex time series is equivalent to a non-periodic signal with continuous frequency spectrum, and is inevitably lost partly by the discrete Fourier transform for the discrete finite time point. Our numerical experiments with natural logarithmic transformation confirm these theoretical deductions.