DA-SPS: A Dual-stage Network based on Singular Spectrum Analysis, Patching-strategy and Spearman-correlation for Multivariate Time-series Prediction

Multivariate time-series forecasting, as a typical problem in the field of time series prediction, has a wide range of applications in weather forecasting, traffic flow prediction, and other scenarios. However, existing works do not effectively consider the impact of extraneous variables on the prediction of the target variable. On the other hand, they fail to fully extract complex sequence information based on various time patterns of the sequences. To address these drawbacks, we propose a DA-SPS model, which adopts different modules for feature extraction based on the information characteristics of different variables. DA-SPS mainly consists of two stages: the target variable processing stage (TVPS) and the extraneous variables processing stage (EVPS). In TVPS, the model first uses Singular Spectrum Analysis (SSA) to process the target variable sequence and then uses Long Short-Term Memory (LSTM) and P-Conv-LSTM which deploys a patching strategy to extract features from trend and seasonality components, respectively. In EVPS, the model filters extraneous variables that have a strong correlation with the target variate by using Spearman correlation analysis and further analyses them using the L-Attention module which consists of LSTM and attention mechanism. Finally, the results obtained by TVPS and EVPS are combined through weighted summation and linear mapping to produce the final prediction. The results on four public datasets demonstrate that the DA-SPS model outperforms existing state-of-the-art methods. Additionally, its performance in real-world scenarios is further validated using a private dataset collected by ourselves, which contains the test items’ information on laptop motherboards.

💡 Research Summary

The paper addresses two major shortcomings of existing multivariate time‑series forecasting (MTSF) approaches: (1) insufficient handling of the influence of extraneous variables on the target variable, and (2) inadequate exploitation of the distinct temporal patterns (trend, seasonality, noise) that naturally exist within each series. To overcome these issues, the authors propose DA‑SPS, a Dual‑stage network that processes the target series and the extraneous series separately before fusing their representations.

In the Target Variable Processing Stage (TVPS), the target series is first decomposed by Singular Spectrum Analysis (SSA) into trend, seasonal, and noise components. The noise component is discarded as interference. The seasonal component, which is relatively regular, is fed into a conventional LSTM to capture long‑range dependencies. The trend component, which may contain more complex, slowly varying patterns, is split into short patches using a “patching strategy”. Each patch is then processed by a Convolutional LSTM (Conv‑LSTM) that can model both spatial (patch‑to‑patch) and temporal relationships. The outputs of the LSTM (seasonality) and Conv‑LSTM (trend) are concatenated and passed through a linear layer to obtain a unified target‑feature vector.

In the Extraneous Variable Processing Stage (EVPS), the model first computes the Spearman rank correlation between each extraneous series and the target series. Only variables whose absolute correlation exceeds a predefined threshold are retained, thereby filtering out weakly related or noisy inputs. The selected variables are fed into an L‑Attention module, which consists of an LSTM encoder followed by an attention mechanism. The LSTM captures the temporal dynamics of each extraneous series, while the attention weights quantify the relevance of each time step and each variable to the target, allowing the network to focus on the most informative cross‑variable interactions.

The two feature vectors (from TVPS and EVPS) are combined by a weighted summation; the weights are learned during training, enabling the model to automatically balance the contributions of trend, seasonality, and extraneous information. The fused representation is finally mapped through a fully‑connected linear layer to produce the forecast for the desired horizon (e.g., 3, 6, 12, or 24 steps ahead).

The authors evaluate DA‑SPS on four public benchmarks (ETTh, ETTm, Traffic, Weather) and a private dataset consisting of laptop motherboard test‑item measurements. Across all datasets, DA‑SPS consistently outperforms state‑of‑the‑art baselines such as LSTNet, Autoformer, Informer, and DCRNN in terms of MAE, RMSE, and MAPE. Ablation studies demonstrate the importance of each component: removing SSA, using raw series instead of patches, omitting the Spearman‑based variable selection, or replacing L‑Attention with a simple concatenation all lead to noticeable performance drops. The experiments also show that the noise‑removal step and the selective inclusion of strongly correlated extraneous variables are the primary drivers of the observed gains.

Complexity analysis indicates that SSA and the patching operation have linear time complexity with respect to the series length, while the L‑Attention module scales with the number of selected extraneous variables, which is kept modest by the correlation filter. Consequently, the overall model remains computationally efficient and suitable for real‑time inference on modern GPUs.

In summary, DA‑SPS introduces a novel combination of (i) explicit time‑series decomposition to isolate predictable components, (ii) rank‑based correlation filtering to prune irrelevant external series, and (iii) a dual‑stage architecture that applies specialized deep‑learning modules (LSTM, Conv‑LSTM, attention‑enhanced LSTM) to capture both intra‑series patterns and inter‑series dependencies. The results validate that this design yields superior forecasting accuracy and robustness, offering a promising direction for future research on more complex, non‑stationary, and high‑dimensional time‑series applications.