Wavelet (EWT and VMD) system and a transformer network that uses the transformation results as input are compared with conventional models in the analysis of time series. The basic idea of these EWT and VMD transformations is to use the Fourier transform and extract information on behavior of time series from the results. The transformations can be applied in different ways: to the series as a whole, separately to the trend and seasonality, etc. Moreover, the components obtained after decomposition can be either assembled back or used in other models to describe the interdependencies in the data of the series. The trend and seasonality can be described using several approaches, in particular, STL transformation, ARIMA/ETS statistical models, trend processing using polynomials, decomposition of seasonality using Fourier series, etc. The approaches can be combined using various models to describe parts of the series (trend, seasonality, and remainder) due to the fact that a single model can describe only a part of time series. For example, ARIMA/ETS statistical models perfectly describe seasonality and remainder having means to describe the trend. Neural network models work better to describe the trend but have problems in seasonality description. A combination of models is assumed to improve the forecasts. In this work, EWT components are used to describe trend and seasonality. The results and the original signal are used as input to neural network models (transformers) forming hybrid models. The forecasts of hybrid models are compared with those of conventional models.
Bakulin et al. (Tue,) studied this question.