  Long-term time series forecasting (LTSF) provides longer insights into future
trends and patterns. Over the past few years, deep learning models especially
Transformers have achieved advanced performance in LTSF tasks. However, LTSF
faces inherent challenges such as long-term dependencies capturing and sparse
semantic characteristics. Recently, a new state space model (SSM) named Mamba
is proposed. With the selective capability on input data and the hardware-aware
parallel computing algorithm, Mamba has shown great potential in balancing
predicting performance and computational efficiency compared to Transformers.
To enhance Mamba's ability to preserve historical information in a longer
range, we design a novel Mamba+ block by adding a forget gate inside Mamba to
selectively combine the new features with the historical features in a
complementary manner. Furthermore, we apply Mamba+ both forward and backward
and propose Bi-Mamba+, aiming to promote the model's ability to capture
interactions among time series elements. Additionally, multivariate time series
data in different scenarios may exhibit varying emphasis on intra- or
inter-series dependencies. Therefore, we propose a series-relation-aware
decider that controls the utilization of channel-independent or channel-mixing
tokenization strategy for specific datasets. Extensive experiments on 8
real-world datasets show that our model achieves more accurate predictions
compared with state-of-the-art methods.
