Leveraging Non-Decimated Wavelet Packet Features and Transformer Models
  for Time Series Forecasting
Guy P Nason James L. Wei
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.