Leveraging Non-Decimated Wavelet Packet Features and Transformer Models for Time Series Forecasting

Abstract: This article combines wavelet analysis techniques with machine learning methods for univariate time series forecasting, focusing on three main contributions. Firstly, we consider the use of Daubechies wavelets with different numbers of vanishing moments as input features to both non-temporal and temporal forecasting methods, by selecting these numbers during the cross-validation phase. Secondly, we compare the use of both the non-decimated wavelet transform and the non-decimated wavelet packet transform for computing these features, the latter providing a much larger set of potentially useful coefficient vectors. The wavelet coefficients are computed using a shifted version of the typical pyramidal algorithm to ensure no leakage of future information into these inputs. Thirdly, we evaluate the use of these wavelet features on a significantly wider set of forecasting methods than previous studies, including both temporal and non-temporal models, and both statistical and deep learning-based methods. The latter include state-of-the-art transformer-based neural network architectures. Our experiments suggest significant benefit in replacing higher-order lagged features with wavelet features across all examined non-temporal methods for one-step-forward forecasting, and modest benefit when used as inputs for temporal deep learning-based models for long-horizon forecasting.