Statistical Lag Screening Boosts Multi-Region Electricity Load Forecasting

A new study published in Energy Informatics reports that a formal multivariate feature selection framework can improve short-term electricity load forecasting across an interconnected power grid. Researchers Yunita Ardilla, Ahmad Saikhu, and Sutikno Sutikno developed a method built on the Partial Lag Correlation Matrix Function (PLCMF), validated through Granger causality testing, and applied it to a gated recurrent unit (GRU) neural network forecasting loads in six regions of Indonesia’s Java–Bali interconnection system. Their evaluation across three distinct test windows showed the proposed model achieved the lowest error in 25 of 54 evaluation scenarios, outperforming both a heuristic sliding-window baseline and a univariate PACF-based approach.

The motivation stems from a persistent gap in the deep learning load forecasting literature. Most studies determine which historical lags to feed into a model using a sliding window, a heuristic whose length is set by trial and error rather than statistical evidence. The authors argue this can introduce lags that carry noise rather than genuine predictive signal, raising overfitting risk. The smaller subset of studies that do perform explicit temporal feature selection has relied predominantly on the univariate Partial Autocorrelation Function (PACF), which by construction can only examine a single series against its own past and is inherently incapable of detecting temporal dependencies between different regions once multivariate confounding effects are controlled for.

PLCMF, formally introduced by Wei in the context of vector autoregression (VAR) identification, generalizes the PACF to the multivariate setting. Instead of producing a scalar per series, it yields a six-by-six matrix at each lag, whose element (i, j) measures the direct partial correlation between region j at time t−k and region i at time t, after simultaneously removing the linear influence of all intermediate lags and all other regional series. The framework applies a dual-confirmation principle: a cross-regional lag enters the model’s input features only if it is significant under PLCMF and also passes a Granger causality test confirming incremental predictive relevance beyond the target region’s own history.

The dataset comprised half-hourly electricity load records, in megawatts, from six Java–Bali subsystems—Krian, Krian-Gresik, Kediri, Paiton, Ngimbang, and Grati—covering January 2023 to October 2025, with 48,912 observations per region. The daily cycle was divided into three intraday periods, and each period was modeled separately after Augmented Dickey-Fuller tests on all 18 series (six regions across three periods) rejected the unit-root null hypothesis at the 1% significance level. The authors deliberately used a load-only framework, excluding weather variables, and acknowledge that shared meteorological drivers could partly manifest as apparent cross-regional dependencies, though they argue the lagged structure and Granger requirement mitigate this concern.

The analysis uncovered dependency structures that varied systematically by period. In period 2 (daytime), a strong negative partial correlation cluster appeared in the region 2 column at lag 8—equivalent to a four-hour offset—with coefficients ranging from −0.23 to −0.35, a pattern the authors interpret as consistent with a load compensation dynamic. In period 3 (night), the largest cross-regional partial correlation in the entire analysis emerged: a value of 0.65 linking region 6 (Grati) to region 4 (Paiton) at lag 1, alongside an opposite-signed reverse link of −0.34, forming an asymmetric bidirectional pair. The authors stress these physical interpretations are plausible hypotheses, not proven mechanisms, since the analysis used only load data without dispatch or transmission records.

Robustness checks supported the statistical screening. Of 1,133 off-diagonal PLCMF elements significant in uncorrected testing across the three periods, 1,121 (98.9%) retained significance after Benjamini-Hochberg false discovery rate correction. Granger causality was significant for all 30 directed region pairs in all three periods (p < 0.001), with the Akaike Information Criterion uniformly selecting a lag order of 10—meaning the Granger criterion acted as a confirmatory filter rather than a discriminatory one, leaving the per-element PLCMF test to determine which specific lags entered the feature set.

Forecasting performance was evaluated with an expanding-window design over three non-overlapping 15-day test windows: August 1–15, 2024; January 1–15, 2025; and October 1–15, 2025. On test data, GRU-PLCMF achieved the lowest RMSE in 25 of 54 scenarios (46.3%), compared with 16 wins for the sliding-window GRU and 13 for the PACF-based GRU, and recorded the most wins in every individual window. The minimum MAPE achieved was 1.81%, in region 4 during period 1 of the October 2025 window. The overall average test MAPE was 5.88% for the proposed model, against 6.45% for the sliding-window variant and 6.58% for the PACF variant.

The largest gains appeared in period 3 of the October 2025 window, where MAPE fell from 5.45% to 1.85% in region 4, from 20.87% to 9.57% in region 5, and showed substantial reductions in regions 2, 3, and 6. Period 2 was the most consistently favorable period, with the proposed model winning 11 of 18 scenarios across all windows—a result the authors link to the lag-8 compensation structure identified only in that period. Test-to-training MAPE ratios also favored the proposed model in these scenarios; in region 4, the sliding-window model’s ratio of 2.84 contrasted with 0.40 for the PLCMF model, a favorable out-of-sample error pattern the authors attribute to statistically validated feature selection, while noting such ratios do not by themselves prove the absence of overfitting.

The study also defines a clear boundary condition. In period 3 of the January 2025 window, coinciding with the post-New Year holiday period, GRU-PLCMF failed to win any of the six regions, with MAPE values ranging from 4.92% to 17.19%. The authors interpret this as an out-of-distribution condition in which the static cross-regional dependency topology, estimated once from the October 2025 window’s training data and held fixed across all windows, no longer matched a structurally shifted consumption pattern. They recommend adaptive feature re-selection and the integration of exogenous calendar variables for such disruption periods.

The authors are explicit about the scope of their claims. The full feature-selection-and-forecasting pipeline is fully prospective only for the October 2025 window; for the two earlier windows, the feature-selection step incorporates data that postdate the test periods, so the three-window evaluation is best read as an assessment of cross-window robustness under a static topology assumption rather than complete out-of-sample validation. The comparison also lacks a true univariate per-region baseline and a direct benchmark against spatio-temporal graph neural networks, both flagged as future work. Within those limits, the study offers empirical evidence that formally validated multivariate lag selection can improve both the accuracy and the interpretability of deep learning models forecasting electricity loads across interconnected regions.

Subject of Research: A multivariate statistical feature selection framework for deep learning forecasting of electricity loads across six interconnected Indonesian grid regions

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

Article References: Ardilla, Y., Saikhu, A., & Sutikno, S. (2026). A dual-confirmation multivariate feature selection framework using partial lag correlation matrix function for multi-region electricity load forecasting. Energy Informatics, 9(1), Article 75. https://doi.org/10.1186/s42162-026-00689-8

Image Credits: AI Generated

DOI: 10.1186/s42162-026-00689-8

Keywords: electricity load forecasting, PLCMF, Granger causality, GRU, feature selection, Java-Bali grid, time series, VAR, deep learning, multi-region forecasting, dual-confirmation, multivariate