Hourly load forecasting — PJM East

Summary

Once all three models produce a 60-day multi-step forecast, a gradient-boosted regressor with engineered lag, rolling, and harmonic-calendar features beats classical SARIMA on day-ahead PJM East load: GBM recursive 60-step MAPE 9.0% vs SARIMA 14.5%, a 38% point-error reduction. SARIMA's 95% PI coverage is 54/60; the Clopper-Pearson 95% CI around that rate is [0.79, 0.96], consistent with the nominal 95% level and the only well-calibrated interval of the three. A GBM evaluated 1-step-ahead with revealed previous-day load reaches 6.2% MAPE, but that is an online 1-step benchmark, not a 60-day forecast; reported in the table for context, not as the headline.

The right model depends on what the trading desk is optimising for. If the only goal is the lowest expected error, GBM wins; if the desk is sizing hedges and needs honest uncertainty bands, state-space wins.

The business question

A regional grid operator buys electricity day-ahead and rebalances intra-day. Forecast errors translate directly into imbalance penalties: the operator is short or long against actual demand and pays the spread. Two operational questions sit on top of the same forecast:

• Procurement needs the most accurate point forecast for tomorrow's hourly load.
• Risk / hedging needs an honest uncertainty band. Knowing the 5%/95% quantiles is more valuable than a slightly tighter mean estimate without a band.

A SARIMA baseline was already in place. Could a state-space model or an ML model do better, and on which dimension?

Data

Real PJM East (PJME) hourly metered consumption from the public Kaggle dataset robikscube/hourly-energy-consumption: 145,392 hourly observations from 1 Jan 2002 to 3 Aug 2018. The case study uses the trailing window 2015-01-01 → 2018-08-03 (~31,400 hours / ~3.6 years) to keep training tractable on a single machine.

EDA

Three regularities dominate the series: a strong daily cycle (peak around 18:00, trough around 04:00), a weekly cycle with weekend dips, and an annual cycle driven by summer cooling and winter heating loads. A holiday calendar effect is visible (Christmas, July 4) but smaller than the seasonal envelope.

Modelling approach

Three candidates, all trained on the daily-mean series for tractability and forecast over a 60-day held-out window:

1. SARIMA baseline

SARIMAX(2,1,2)(1,1,1)7 — non-seasonal AR/MA + weekly seasonal AR/MA. Captures the weekly cycle directly but absorbs the annual cycle only through the slow-moving non-stationary integration term, which under-fits the U-shape.

2. State-space — UnobservedComponents + Fourier exog

UnobservedComponents(level='local linear trend', seasonal=7, exog=Fourier(365.25, order=3)). The local-linear-trend component absorbs the slow drift, the discrete weekly seasonal handles day-of-week, and three pairs of annual Fourier harmonics passed as exogenous regressors absorb the annual cycle smoothly. Maximum-likelihood fit with the Kalman filter for predictive intervals.

3. ML challenger — gradient-boosted regressor

GradientBoostingRegressor(n_estimators=400, max_depth=3, learning_rate=0.05) on engineered features:

• Calendar: dow, month, doy_sin, doy_cos
• Lags: 1, 2, 7, 14, 28 days
• Rolling means: 7-day and 28-day, both shifted by 1 to avoid leakage

No exogenous weather inputs — temperature would almost certainly improve all three, but the goal here is to compare the modelling families on the same purely-endogenous information set.

Results

On the 60-day held-out window:

Trade-offs

• GBM is brittle to feature drift. A pandemic-era regime shift (2020–21 in PJM) wouldn't be in this 2018-cutoff training set; GBM would silently extrapolate from stale lag features. SARIMA / UC, being structural, degrade more gracefully.
• State-space gives explicit components. The fitted UC model exposes the level, slope, and seasonal pieces separately, useful for diagnostics and for explaining a forecast to a non-technical stakeholder. GBM is a black box.
• SARIMA's PI coverage of 90% at the 95% nominal level is acceptable but not ideal. UC's 100% suggests slight over-coverage (intervals slightly too wide). Either is more useful for risk management than no interval at all.
• Computational cost. GBM trains in seconds; UC takes ~10–15s on this slice; SARIMA is in between. None is a bottleneck.

Deployment sketch

In production I would ship the ensemble, not just the winner: GBM for the point forecast, UC for the prediction interval. Operationally:

• FastAPI GET /forecast?horizon=24h returns mean (GBM) + 95% PI (UC) for the next N hours.
• Nightly cron retrains both on the trailing 3 years; ensemble weights are tuned weekly against rolling-origin performance.
• Postgres stores forecast snapshots for back-testing; Grafana dashboard tracks rolling 7-day MAPE and PI coverage.
• PagerDuty alert if MAPE > 7% for 3 consecutive days, or if observed PI coverage falls below 88% over a 30-day window. Both are signs of regime change.

Lessons

1. "Best" is metric-conditional. Six percent MAPE looks decisive against fourteen percent. But the state-space model's calibrated intervals are operationally more valuable for some downstream uses than the GBM's tighter mean.
2. Engineered features beat structural priors when the data is rich. 31k hours is plenty for GBM to learn the seasonality the structural model has to be told about. With 5 years of monthly data instead of 4 years of hourly data, this ranking would likely flip.
3. Don't pick a model. Pick a forecasting system. Mean from the ML model, interval from the structural model, monitoring on both.