  Time series data, including univariate and multivariate ones, are
characterized by unique composition and complex multi-scale temporal
variations. They often require special consideration of decomposition and
multi-scale modeling to analyze. Existing deep learning methods on this best
fit to univariate time series only, and have not sufficiently considered
sub-series modeling and decomposition completeness. To address these
challenges, we propose MSD-Mixer, a Multi-Scale Decomposition MLP-Mixer, which
learns to explicitly decompose and represent the input time series in its
different layers. To handle the multi-scale temporal patterns and multivariate
dependencies, we propose a novel temporal patching approach to model the time
series as multi-scale patches, and employ MLPs to capture intra- and
inter-patch variations and channel-wise correlations. In addition, we propose a
novel loss function to constrain both the mean and the autocorrelation of the
decomposition residual for better decomposition completeness. Through extensive
experiments on various real-world datasets for five common time series analysis
tasks, we demonstrate that MSD-Mixer consistently and significantly outperforms
other state-of-the-art algorithms with better efficiency.
