  Transformer-based models have emerged as promising tools for time series
forecasting.
  However, these model cannot make accurate prediction for long input time
series. On the one hand, they failed to capture global dependencies within time
series data. On the other hand, the long input sequence usually leads to large
model size and high time complexity.
  To address these limitations, we present GCformer, which combines a
structured global convolutional branch for processing long input sequences with
a local Transformer-based branch for capturing short, recent signals. A
cohesive framework for a global convolution kernel has been introduced,
utilizing three distinct parameterization methods. The selected structured
convolutional kernel in the global branch has been specifically crafted with
sublinear complexity, thereby allowing for the efficient and effective
processing of lengthy and noisy input signals. Empirical studies on six
benchmark datasets demonstrate that GCformer outperforms state-of-the-art
methods, reducing MSE error in multivariate time series benchmarks by 4.38% and
model parameters by 61.92%. In particular, the global convolutional branch can
serve as a plug-in block to enhance the performance of other models, with an
average improvement of 31.93\%, including various recently published
Transformer-based models. Our code is publicly available at
https://github.com/zyj-111/GCformer.
