  Recently, significant advancements have been made in time-series forecasting
research, with an increasing focus on analyzing the nature of time-series data,
e.g, channel-independence (CI) and channel-dependence (CD), rather than solely
focusing on designing sophisticated forecasting models. However, current
research has primarily focused on either CI or CD in isolation, and the
challenge of effectively combining these two opposing properties to achieve a
synergistic effect remains an unresolved issue. In this paper, we carefully
examine the opposing properties of CI and CD, and raise a practical question
that has not been effectively answered, e.g.,"How to effectively mix the CI and
CD properties of time series to achieve better predictive performance?" To
answer this question, we propose Mlinear (MIX-Linear), a simple yet effective
method based mainly on linear layers. The design philosophy of Mlinear mainly
includes two aspects:(1) dynamically tuning the CI and CD properties based on
the time semantics of different input time series, and (2) providing deep
supervision to adjust the individual performance of the "CI predictor" and "CD
predictor". In addition, empirically, we introduce a new loss function that
significantly outperforms the widely used mean squared error (MSE) on multiple
datasets. Experiments on time-series datasets covering multiple fields and
widely used have demonstrated the superiority of our method over PatchTST which
is the lateset Transformer-based method in terms of the MSE and MAE metrics on
7 datasets with identical sequence inputs (336 or 512). Specifically, our
method significantly outperforms PatchTST with a ratio of 21:3 at 336 sequence
length input and 29:10 at 512 sequence length input. Additionally, our approach
has a 10 $\times$ efficiency advantage at the unit level, taking into account
both training and inference times.

Machine Learning;Artificial Intelligence