# Addressing the Non-Stationarity and Complexity of Time Series Data for Long-Term Forecasts
## 4 Conclusions  
This study proposed a deep learning architecture designed to address the challenges of TSF in both multivariate and univariate settings. It focuses on the non-stationary nature of real-world time series data as well as the complexities of intra- and inter-series relationships. The suggested architecture comprises novel components such as the \"weak  
Figure 3: Run-time requirement and memory consumption analysis while varying FHL and LWL. A comparison was made among Autoformer, Informer, transformer, and our method (with the number of layers ranging from one to five) on a log-scale. (**a**) Comparison of GPU memory consumption while varying the FHL; (**b**) comparison of GPU memory consumption while varying the LWL; (**c**) comparison of time taken for execution while varying the FHL; (**d**) comparison of time taken for execution while varying the LWL.  
stationarizing\" block and \"non-stationarity restoring\" block to handle non-stationarity, while also leveraging spectral decomposition and a ConvMixer architecture to capture complex relations within the data. The experimental results demonstrate the effectiveness of the proposed model across six real-world datasets, achieving superior or comparable performance to SOTA methods in most cases. Additionally, the proposed model requires significantly less memory and execution time compared to other transformer-based models. This makes the model suitable for usage in scenarios where the computation resources are limited. Although the focus is on long-sequence time series, the model is adaptable to short-sequence scenarios as well. Moving forward, it would be interesting to explore how the concepts introduced in the proposed model can complement existing forecasting models, such as transformers, TCNs, and RNNs. Additionally, there is room for improvement in handling datasets without seasonality, suggesting avenues for further research to enhance the model's performance in such scenarios.  
Conceptualization, R.B.; methodology, R.B.; software, R.B.; validation, R.B. and S.-W.L.; formal analysis, R.B.; investigation, R.B.; resources, S.-W.L.; data curation, R.B.; writing--original draft preparation, R.B.; writing--review and editing, R.B. and S.-W.L.; visualization, S.-W.L.; supervision, S.-W.L.; project administration, S.-W.L.; funding acquisition, S.-W.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Gachon University research fund of 2020(202008450003) and the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIT) (No. RS-2023-00250978).  
Not applicable.  
All the datasets used in this paper are publicly available datasets and all of them have been cited above.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} TSF & Time series forecasting \\ ARIMA & Auto regressive integrated moving average \\ LSTF & Long-sequence time series forecasting \\ TCN & Temporal convolutional network \\ PSD & Power spectral density \\ FFT & Fast Fourier transform \\ DFFT & Discrete fast Fourier transform \\ SOTA & State of the art \\ RNN & Recurrent neural network \\ DA & Domain adaptation \\ DG & Domain generalization \\ GNN & Graph neural network \\ ORV & Optimum roll back value \\ WSO & Weak-stationary output \\ NSO & Non-stationary output \\ WS & Weak stationarizing \\ NSR & Non-stationarity restoring \\ DW & Depthwise convolution \\ PW & Pointwise convolution \\ LWL & Look-back window length \\ MSE & Mean squared error \\ MAE & Mean average error \\ \end{tabular}