A dual-confirmation multivariate feature selection framework using partial lag correlation matrix function for multi-region electricity load forecasting

Short-term electricity load forecasting in multi-region systems is a critical challenge in power grid management, particularly in heterogeneous interconnected systems with temporal dependencies between subsystems. While most deep learning studies for electricity load forecasting rely on heuristic sliding window approaches without any formal feature selection, the subset of studies that explicitly perform temporal feature selection has been predominantly limited to univariate Partial Autocorrelation Function (PACF), an approach inherently incapable of detecting cross-regional temporal dependencies once multivariate confounding effects are controlled for. This study proposes a multivariate temporal feature selection framework based on the Partial Lag Correlation Matrix Function (PLCMF), a formal multivariate generalization of PACF in a vector autoregression framework validated through the Granger Causality test as a dual-confirmation principle. Only cross-regional lags that simultaneously satisfy both conditions of direct partial dependency significance (PLCMF) and incremental predictive relevance (Granger) are integrated as input features of a gated recurrent unit model with a multi-input multi-output architecture. The evaluation results on the test data show that GRU-PLCMF outperforms GRU with a sliding window (GRU-SW) and GRU with univariate PACF (GRU-PACF) in 25 of the 54 evaluation scenarios across three distinct test windows, with a minimum MAPE value of 1.81%. The PLCMF analysis successfully identified partial dependency structures that varied systematically across periods, including cross-regional load compensation phenomena and asymmetric bidirectional dependency patterns, which could not be detected by univariate or sliding window approaches. These findings provide empirical evidence that the integration of a multivariate statistics-based temporal feature selection framework improves the out-of-sample forecasting accuracy of the GRU model and the interpretability of the cross-regional feature selection structure used for simultaneous multi-region electricity load forecasting.