cs.LGOct 8, 2026
SaveMachine Learning and Time-Series Foundation Models for Day-Ahead Electricity Forecasting in a University Building
Abstract
Day-ahead electricity forecasts can help building operators schedule heating, ventilation, and other services around anticipated demand. Choosing a forecasting model also requires balancing accuracy with its forecast-time inputs, local training, and computational requirements. We benchmark statistical, machine-learning, recurrent neural-network, and pretrained TimesFM models for a university building. We use chronological validation and evaluate all configurations on the same 57 test days, comparing accuracy across workdays, weekends, and holidays alongside local fitting and forecasting time. Weather covariates use retrospective observations. TimesFM 3.0 with covariates achieves the lowest overall errors, reducing mean absolute error by approximately 43% relative to weekly seasonal-naive forecasting. XGBoost remains competitive, although paired daily comparisons do not establish a clear mean-absolute-error advantage for TimesFM. TimesFM also performs strongly using only past electricity consumption. Adding covariates improves its holiday forecasts but slightly worsens workday and weekend forecasts, leaving overall mean absolute error almost unchanged. TimesFM requires no building-specific weight training, while XGBoost offers rapid local fitting and inference. The evaluated LSTM takes longer to fit without outperforming either approach. An exploratory historical evaluation reveals seasonal variation, while a separate weather-source comparison produces only small changes in the selected TimesFM configuration's accuracy. These results support pretrained TimesFM as a strong initial forecasting baseline for this building, with XGBoost as a competitive locally fitted alternative. Covariates are particularly useful when improved holiday forecasts justify the additional input preparation.
Figures & tables
Figure 1: Whole-building hourly electricity consumption from 4 September 2022 at 23:00 UTC to 30 March 2024 at 22:00 UTC. The upper panel marks the validation and test periods; the lower panel expands the first complete Monday–Sunday week in UTC to show the hourly variation. Both panels retain the original hourly resolution.
| Source | Product | Role in the comparison |
|---|---|---|
| KNMI | Observations at Rotterdam Airport station 344 | Observed-weather reference |
| ERA5 | Gridded reanalysis | Retrospective weather reconstruction |
| Historical IFS | Archived ECMWF IFS forecasts from Open-Meteo | Forecast-product substitution |
Table 1: Weather sources and their role. The main 11-model benchmark uses KNMI for weather covariates; the additional source comparison uses a fixed TimesFM 3.0 configuration.
| Domain | Covariates (number) | Units | Availability |
|---|---|---|---|
| Calendar and schedule (21) | Hour, year, month, week, day, day of week (6) | Calendar indices | Known in advance |
| Sine/cosine pairs for hour, day, day of week, week, month (10) | Dimensionless | Known in advance | |
| Work-week, weekend, holiday, opening-hours, examination-week indicators (5) | Binary | Calendar known; schedules assumed known | |
| Weather (7) | Air and dew-point temperatures (2) | °C | Retrospective |
| Relative humidity; sea-level pressure (2) | %; hPa | Retrospective | |
| Hourly precipitation (1) | mm | Retrospective |
Table 2: The 30 retained covariates, grouped into three domains. Availability refers to the forecast origin. Appendix Section Covariate Catalogue gives the individual stored variables.
| Configuration | Forecast-time inputs | Building-specific fitting |
|---|---|---|
| Seasonal-naive 24 h | Previous day’s consumption at the corresponding hour | None |
| Seasonal-naive 168 h | Previous week’s consumption at the corresponding hour | None |
| Ridge | 30 covariates | Standardisation and regression fitted at each origin |
| XGBoost | 30 covariates | Regression trees fitted at each origin |
| Prophet base | Past consumption and native calendar/holiday components | Trend, seasonality, and holiday effects fitted at each origin |
| Prophet with regressors | Past consumption, 29 external covariates, and native holiday effects | Prophet and its regressors fitted jointly at each origin |
Table 3: Models and their forecast-time inputs. Prophet represents the holiday indicator through its native holiday component, leaving 29 external regressors.
| Stage | Target interval in UTC | Forecast days | Hourly targets | Purpose |
|---|---|---|---|---|
| Initial history | 4 September 2022, 23:00–4 November 2023, 22:00 | 426 | 10,224 | Supply past observations for subsequent forecasts |
| Validation | 4 November 2023, 23:00–2 February 2024, 22:00 | 90 | 2,160 | Select hyperparameters |
| Test | 2 February 2024, 23:00–30 March 2024, 22:00 | 57 | 1,368 | Evaluate the selected configurations |
Table 4: Chronological evaluation periods. Each forecast day begins at 23:00 UTC and contains 24 consecutive targets.
| Group | Hourly observations | Mean (kWh) | Median (kWh) | SD (kWh) | Minimum (kWh) | Maximum (kWh) |
|---|---|---|---|---|---|---|
| Full series | 13752.0 | 140.31 | 112.15 | 76.86 | 13.90 | 452.00 |
| Holiday | 2760 | 87.77 | 77.10 | 33.57 | 13.90 | 374.30 |
| Weekday | 8040 | 176.23 | 161.25 | 79.16 | 56.30 | 452.00 |
| Weekend | 2952 | 91.58 | 83.00 | 30.47 | 46.10 | 306.10 |
Table 5: Electricity-consumption summary over the complete dataset. Consumption values are kWh per hourly interval. Workdays exclude weekends and holidays; holiday labels take precedence.
Figure 2: Mean hourly electricity-consumption profiles for workdays, weekends, and institutional holidays over the complete dataset. Direct labels and distinct line styles identify the three groups. Hours are reported in UTC; the original operating-day memberships are retained.
Figure 3: Pearson correlations between the 30 retained covariates and electricity consumption over the complete dataset. The calendar/schedule, weather, and historical-consumption panels use a common correlation scale and consistent bar thickness; the zero line separates positive and negative associations. Target-day weather is retrospective.
| Model | Forecast-time inputs | MAE (kWh) | RMSE (kWh) | R² | MAPE (%) | sMAPE (%) |
|---|---|---|---|---|---|---|
| TimesFM 3.0 with covariates | Calendar, lags and observed weather | 19.97 | 30.26 | 0.798 | 16.94 | 15.27 |
| TimesFM 3.0 target-only | Past consumption | 20.01 | 32.45 | 0.768 | 16.99 | 14.94 |
| TimesFM 2.5 target-only | Past consumption | 21.07 | 31.85 | 0.777 | 18.50 | 16.09 |
| XGBoost | Calendar, lags and observed weather | 22.45 | 31.11 | 0.787 | 18.98 | 16.86 |
| Prophet with regressors | Calendar, lags and observed weather | 24.91 | 34.22 | 0.742 | 21.39 | 19.73 |
| Ridge | Calendar, lags and observed weather | 27.18 | 37.87 | 0.684 | 22.93 | 20.43 |
Table 6: Test accuracy for the 11 model configurations. MAE and RMSE are in kWh; lower errors and higher are better. Weather covariates use KNMI observations as supplied in the original benchmark.
Figure 4: Pooled MAE and RMSE on the 1,368 common test targets, with configurations ordered by increasing MAE from top to bottom in both panels. Points further left indicate lower error. Colours and marker shapes distinguish TimesFM configurations, XGBoost, and the supporting comparisons; every configuration is labelled.
| Model | Reference | Mean daily-MAE difference (kWh) | 95% percentile CI (kWh) | Paired days |
|---|---|---|---|---|
| Seasonal-naive 24 h | XGBoost | 15.12 | [8.338, 22.252] | 57 |
| Seasonal-naive 168 h | XGBoost | 12.82 | [8.421, 17.742] | 57 |
| Ridge | XGBoost | 4.73 | [2.841, 6.671] | 57 |
| Prophet base | XGBoost | 7.76 | [4.260, 10.958] | 57 |
| Prophet with regressors | XGBoost | 2.46 | [0.422, 4.622] | 57 |
| TimesFM 2.5 target-only | XGBoost | -1.38 | [-4.636, 2.218] | 57 |
Table 7: Mean daily-MAE differences from XGBoost and 95% paired bootstrap intervals, in kWh. Negative differences favour the listed model; positive differences favour XGBoost.
Figure 5: Mean differences in daily MAE and their 95% bootstrap intervals. The all-model comparison uses XGBoost as the reference; the additional panel compares TimesFM configurations directly. Differences are the named model minus its reference, so negative values favour the named model. An interval crossing zero does not establish a direction of improvement.
| Model | Workday MAE (kWh) | Workday RMSE (kWh) | Non-workday MAE (kWh) | Non-workday RMSE (kWh) |
|---|---|---|---|---|
| TimesFM 3.0 with covariates | 18.85 | 26.00 | 21.63 | 35.63 |
| TimesFM 3.0 target-only | 16.65 | 23.00 | 24.98 | 42.75 |
| TimesFM 2.5 target-only | 17.71 | 23.25 | 26.03 | 41.41 |
| XGBoost | 22.88 | 32.15 | 21.81 | 29.50 |
| Prophet with regressors | 23.18 | 31.56 | 27.47 | 37.80 |
| Ridge | 27.41 | 37.88 | 26.84 | 37.85 |
Table 8: Pooled test errors by day type, in kWh. Subgroup rankings describe the observed errors and have not been tested for statistical significance.
Figure 6: MAE and RMSE for TimesFM 2.5, TimesFM 3.0 with and without covariates, and XGBoost, evaluated separately on 34 workdays, 12 weekend days, and 11 holidays. Model settings are identical across groups. Each metric uses a common scale across the three day types; subgroup differences are descriptive.
Figure 7: Observed electricity consumption and frozen TimesFM 3.0 and XGBoost forecasts for the first chronological test forecast origin in each day-type group. The origin labels are in UTC, and each panel contains the corresponding 24 hourly targets on a common consumption scale. Black identifies observations; colour and line style identify the forecasts. The selection rule does not use forecast errors.
| Scenario | n | MAE | RMSE | R² | p95 absolute error |
|---|---|---|---|---|---|
| TimesFM 3.0 with covariates | 13584 | 16.6 | 26.74 | 0.879 | 48.52 |
| Seasonal-naive 168 h | 13584 | 29.16 | 49.03 | 0.593 | 115.38 |
Table 9: Extended historical evaluation on 13,584 common target hours. Error values are in kWh. The TimesFM settings were selected using later validation data; these scores are exploratory.
Figure 8: Monthly pooled MAE and RMSE for TimesFM 3.0 with covariates and the weekly seasonal-naive forecast during the exploratory historical evaluation. The aligned panels share a chronological month axis, and the two models use different line styles and markers. Months refer to UTC target timestamps; September 2022 and March 2024 are partial months.
| Source | Target hours | MAE (kWh) | RMSE (kWh) | R² | MAPE (%) | sMAPE (%) |
|---|---|---|---|---|---|---|
| KNMI station 344 | 1368 | 19.9682 | 30.2878 | 0.7981 | 16.9134 | 15.2548 |
| ERA5 reanalysis | 1368 | 19.968 | 30.2208 | 0.799 | 16.9045 | 15.2468 |
| Historical IFS | 1368 | 20.1373 | 30.4094 | 0.7965 | 17.1393 | 15.389 |
Table 10: Fixed TimesFM 3.0 weather-source comparison using the same UTC hourly intervals. Context, other covariates, and model settings are held constant. This KNMI result uses the supplementary interval assignment and is distinct from the original benchmark row.
Figure 9: Paired differences in daily MAE between weather sources, with 95% day-block bootstrap intervals. The zero line denotes no difference; a positive value indicates larger error for the first source named. All comparisons use the same 57 forecast windows and fixed TimesFM 3.0 settings. Absolute error values are reported in Table 10 .
| Model | Fit/update median / p95 (s) | Warm 24-h inference median / p95 (s) | Peak RSS (MiB) | Peak GPU allocated (MiB) |
|---|---|---|---|---|
| TimesFM 3.0 with covariates | 0.000000 / 0.000000 | 0.9215 / 0.9680 | 4402.73 | 2470.39 |
| TimesFM 3.0 target-only | 0.000000 / 0.000000 | 0.4047 / 0.4566 | 4402.73 | 1308.73 |
| TimesFM 2.5 target-only | 0.000000 / 0.000000 | 0.1197 / 0.1394 | 2435.05 | 898.29 |
| XGBoost | 0.8418 / 3.43 | 0.001232 / 0.004213 | 378.00 | not applicable |
| Prophet with regressors | 4.19 / 5.97 | 0.3201 / 0.3582 | 254.04 | not applicable |
| Ridge | 0.0302 / 0.0359 | 0.002373 / 0.003514 | 191.07 | not applicable |
Table 11: Measured time and memory during test forecasting. Times are seconds per 24-hour forecast origin, summarised by median and 95th percentile. The LSTM ridge-correction row is additional to the LSTM base cost.
| Source identifier(s) | Scientific meaning | Domain | Unit or encoding |
|---|---|---|---|
| Exam_weeks | Exam-week indicator | calendar/schedule | binary |
| Opening_hours | Opening-hours indicator | calendar/schedule | binary |
| Hour | Hour label | calendar/schedule | hour |
| Year | Calendar year | calendar/schedule | year |
| Month | Calendar month | calendar/schedule | month |
| Week | ISO week number | calendar/schedule | week |
Table 12: Stored names, scientific meanings, and units for the 30 retained covariates. The manuscript uses the scientific names; the stored names enable reproduction.
| Model | Validation trials | Validation MAE (kWh) | Validation RMSE (kWh) | Validation R² | Selected parameter details |
|---|---|---|---|---|---|
| TimesFM 3.0 with covariates | 64 | 19.98 | 28.90 | 0.861 | context_values=8760; make_positive=False; point_forecast=median_quantile_index_4; return_quantiles=True; use_symmetric_averaging=True; use_znorm=False |
| TimesFM 3.0 target-only | 64 | 19.37 | 28.64 | 0.863 | context_values=8760; make_positive=False; point_forecast=median_quantile_index_4; return_quantiles=True; use_symmetric_averaging=True; use_znorm=False |
| TimesFM 2.5 target-only | 8 | 23.38 | 36.26 | 0.781 | context_values=672; normalize_inputs=False |
| XGBoost | 96 | 21.27 | 28.76 | 0.862 | colsample_bytree=0.6239; learning_rate=0.01401; max_depth=7; min_child_weight=0.999; n_estimators=1350; reg_alpha=0.4845; reg_lambda=0.05573; subsample=0.7332 |
| Prophet with regressors | 96 | 24.13 | 32.16 | 0.827 | changepoint_prior_scale=0.01784; changepoint_range=0.8846; daily_fourier_order=10; daily_mode=additive; holidays_prior_scale=4.843; regressor_prior_scale=0.02489; seasonality_prior_scale=0.1609; weekly_fourier_order=7; weekly_mode=additive |
| Ridge | 25 | 26.82 | 35.69 | 0.787 | alpha=215.4 |
Table 13: Validation scores and selected settings for the benchmark configurations. Every candidate was evaluated on 2,160 hourly validation targets.
Figure 10: MAE and RMSE for all 11 configurations on workdays, weekends, and holidays. Model ordering is identical across panels, and each metric uses the same scale across day types. Counts are 34 workdays, 12 weekend days, and 11 holidays.
| Configuration | Validation MAE (kWh) | Validation RMSE (kWh) | Test MAE (kWh) | Test RMSE (kWh) |
|---|---|---|---|---|
| TimesFM 2.5 target-only | 23.38 | 36.26 | 21.07 | 31.85 |
| TimesFM 2.5 + ridge residual (jointly tuned) | 23.77 | 36.30 | 20.88 | 31.44 |
| Ridge + TimesFM 2.5 residual (jointly tuned) | 22.54 | 31.66 | 25.14 | 34.91 |
Table 14: Validation and test errors for TimesFM 2.5 target-only and the two jointly tuned hybrids. Validation covers 2,160 target hours and testing 1,368; all errors are in kWh.
| Group | Level | Model | Target hours | MAE (kWh) | RMSE (kWh) |
|---|---|---|---|---|---|
| Day type | holiday | TimesFM 3.0 with covariates | 2760 | 17.887 | 34.969 |
| Day type | weekend | TimesFM 3.0 with covariates | 2904 | 14.648 | 25.227 |
| Day type | workday | TimesFM 3.0 with covariates | 7920 | 16.863 | 23.81 |
| Day type | holiday | Seasonal-naive 168 h | 2760 | 40.62 | 69.059 |
| Day type | weekend | Seasonal-naive 168 h | 2904 | 20.574 | 35.139 |
| Day type | workday | Seasonal-naive 168 h | 7920 | 28.317 | 44.806 |
Table 15: Historical evaluation by day type and meteorological season. MAE and RMSE are in kWh; target-hour counts identify the coverage of each group.
| UTC month | Target hours | Context min | Context max | MAE (kWh) | RMSE (kWh) | Naive MAE (kWh) | Naive RMSE (kWh) |
|---|---|---|---|---|---|---|---|
| 2022-09 | 457 | 168 | 624 | 10.519 | 14.674 | 10.82 | 14.428 |
| 2022-10 | 744 | 624 | 1368 | 10.169 | 19.31 | 18.163 | 35.337 |
| 2022-11 | 720 | 1368 | 2088 | 19.474 | 31.703 | 30.046 | 45.45 |
| 2022-12 | 744 | 2088 | 2832 | 17.181 | 23.717 | 44.034 | 68.687 |
| 2023-01 | 744 | 2832 | 3576 | 19.842 | 26.994 | 40.608 | 59.109 |
| 2023-02 | 672 | 3576 | 4248 | 18.398 | 27.194 | 30.404 | 46.698 |
Table 16: Chronological monthly errors and context coverage. Context ranges are the minimum and maximum numbers of prior hourly observations supplied to TimesFM for forecasts contributing to the UTC month.
| Contrast | Origin days | Estimate (kWh) | 95% CI low (kWh) | 95% CI high (kWh) |
|---|---|---|---|---|
| ERA5 reanalysis − KNMI station 344 | 57 | -0.0002 | -0.1672 | 0.1706 |
| Historical IFS − KNMI station 344 | 57 | 0.1691 | 0.0071 | 0.3305 |
| Historical IFS − ERA5 reanalysis | 57 | 0.1693 | 0.0027 | 0.3249 |
Table 17: Paired daily-MAE differences between weather sources, in kWh, with 95% percentile intervals from 10,000 resamples of the 57 forecast-day blocks. Positive values favour the second source named.
| Source | Day type | Target hours | MAE (kWh) | RMSE (kWh) |
|---|---|---|---|---|
| KNMI station 344 | holiday | 264 | 24.741 | 39.332 |
| KNMI station 344 | weekend | 288 | 18.783 | 31.84 |
| KNMI station 344 | workday | 816 | 18.842 | 26.069 |
| ERA5 reanalysis | holiday | 264 | 24.965 | 39.621 |
| ERA5 reanalysis | weekend | 288 | 18.461 | 31.488 |
| ERA5 reanalysis | workday | 816 | 18.883 | 25.948 |
Table 18: Weather-source errors by operating day type. Each source is evaluated on 816 workday, 288 weekend, and 264 holiday target hours.
Figure 11: MAE and RMSE for each weather source on workdays, weekends, and holidays. Within each group, distinct markers identify KNMI, ERA5, and historical IFS on the same error scale. All sources use the same target hours: 816 workday, 288 weekend, and 264 holiday hours.
| Source | UTC month / season | Target hours | MAE (kWh) | RMSE (kWh) |
|---|---|---|---|---|
| KNMI station 344 | February 2024 / DJF | 649 | 23.0108 | 34.7614 |
| KNMI station 344 | March 2024 / MAM | 719 | 17.2218 | 25.5866 |
| ERA5 reanalysis | February 2024 / DJF | 649 | 23.061 | 34.7231 |
| ERA5 reanalysis | March 2024 / MAM | 719 | 17.1761 | 25.4828 |
| Historical IFS | February 2024 / DJF | 649 | 23.1571 | 34.7774 |
| Historical IFS | March 2024 / MAM | 719 | 17.4115 | 25.8402 |
Table 19: Weather-source errors by UTC month and meteorological season. This test contains only February 2024 (649 winter target hours) and March 2024 (719 spring target hours); month and season therefore identify the same two groups.
Figure 12: Autocorrelation of hourly electricity consumption through 336 hours. The highlighted 24- and 168-hour lags identify daily and weekly recurrence, supporting the seasonal-naive references.
Figure 13: Mean hourly electricity consumption over the complete dataset.
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