Extension Methods for Non-stationary Time Series Based on Wavelet Analysis

This study performed extensions of non-stationary time series based on wavelet analysis. The spectrum from the univariate wavelet analysis of raw time series was extended for a hypothetical long-term, and an inverse transform method was adopted. Three methods considered for spectral extraction were “Method (1): randomized by setting different block lengths for each scale,” “Method (2): randomized by setting the same block length for all scales,” and “Method (3): simultaneously randomized by setting same block length for all scales.” To verify these methods, we generated non-stationary time series through nonlinear moving average and nonlinear autoregressive models. The application results of the time series were compared with the distribution and bivariate analysis results of the raw data. Method (1) and (2) exhibited a part that could not mimic the raw data distribution owing to various reasons, such as the disconnection of the spectrum. However, bivariate wavelet analysis confirmed that the raw data distribution and co-movement characteristics of the spectrum could be sufficiently preserved in Method (3).