Multivariate Time Series Long-Term Forecasting Model Based on Sequence Decomposition and Timestamp Feature Coding

In multivariate time series forecasting, many studies have adopted hybrid deep learning methods, in which sequence decomposition is often used, but the traditional moving average decomposition method is insensitive to mutation data and cannot accurately decompose the trend and seasonal components, thus affecting the accuracy of long-term forecasting. Also, some long-term forecasting studies lack timestamped feature encoding modules, limiting the long-term forecasting ability of the models. To address the above issues, this paper proposes a long-term forecasting model. The model first utilizes the exponential moving average decomposition method to decompose the multivariate time series into trend components and seasonal components. The methodology gives more weight to recent data, captures data trends more sensitively, reflects new information in a timely manner, and tracks fluctuations more accurately and in a timely manner than the ordinary moving average method. For the seasonal components, stationary and non-stationary series are obtained by filtering them with the designed seasonal filtering module. Then the stationary and non-stationary series are separately feature extracted and fused to output seasonal forecasts. For the trend components, the trend features are captured by the designed multi-layer perceptual network structure containing GeLU. A timestamp feature coding module is also introduced, this module transforms the temporal information in the time series data into the process of numerical features that can be understood by the model, it can be able to effectively capture the temporal periodicity law, deeply excavate the potential information of the time dimension, and improve the prediction accuracy. The output of which is weighted and fused with the seasonal forecast output, and finally summed with the trend term forecast output to obtain the final long-term forecast output. Comparative experiments on six publicly available longterm prediction datasets show that the average prediction accuracies of the models in this paper are improved by $5.71 \%$, $12.64 \%$, $78.23 \%$, $20.41 \%$, $78.78 \%$, $16.37 \%$, and $6.38 \%$ compared to PatchTST, FEDformer, Informer, TiDE, LSTM, DLinear and LSTM models, respectively.