A Spatial–Temporal Time Series Decomposition for Improving Independent Channel Forecasting

Forecasting multivariate time series is a pivotal task in controlling multi-sensor systems. The joint forecasting of all channels may be too complex, whereas forecasting the channels independently may cause important spatial inter-dependencies to be overlooked. In this paper, we improve the performance of single-channel forecasting algorithms by designing an interpretable front-end that extracts the spatial–temporal components from the input multivariate time series. Specifically, the multivariate samples are first segmented into equal-sized matrix symbols. The symbols are decomposed into the frequency-separated Intrinsic Mode Functions (IMFs) using a 2D Empirical-Mode Decomposition (EMD). The IMF components in each channel are then forecasted independently using relatively simple univariate predictors (UPs) such as DLinear, FITS, and TCN. The symbol size is determined to maximize the temporal stationarity of the EMD residual trend using Bayesian optimization. In addition, since the overall performance is usually dominated by a few of the weakest predictors, it is shown that the forecasting accuracy can be further improved by reordering the corresponding channels to make more correlated channels more adjacent. However, channel reordering requires retraining the affected predictors. The main advantage of the proposed forecasting framework for multivariate time series is that it retains the interpretability and simplicity of single-channel forecasting methods while improving their accuracy by capturing information about the spatial-channel dependencies. This has been demonstrated numerically assuming a 64-channel EEG dataset.