Scalers and VSTs

Every model scales each task’s data before the fit and maps the prediction back afterwards. The model’s scaler parameter chooses how. Besides plain standardisation there are two variance-stabilising transformations (VSTs), which damp price spikes and work with negative prices.

from epftoolbox2.models import OLSModel, LassoCVModel

ols = OLSModel(predictors, name="OLS")                            # scaler="standard" (default)
ols_asinh = OLSModel(predictors, name="OLS asinh", scaler="asinh")
lasso_npit = LassoCVModel(predictors, name="Lasso N-PIT", scaler="npit")

# With parameters: transform only the target and the price lags
lasso_price_vst = LassoCVModel(
    predictors,
    name="Lasso asinh prices",
    scaler={"name": "asinh", "params": {"apply_to": ["price", "price_d-*"]}},
)

A scaler instance works too, e.g. scaler=AsinhScaler(apply_to="target") with from epftoolbox2.scalers import AsinhScaler. The model stores it as a {"name", "params"} dict so the pipeline can be saved to YAML. Only the scalers listed below are accepted.

Available scalers

scaler	Class	Transformation of a column x (parameters from the training rows)
"standard"	StandardScaler	(x - mean) / sd
"asinh"	AsinhScaler	asinh((x - median) / (MAD / 0.6745)), then standardised
"npit"	NPITScaler	Φ⁻¹(F̂(x)) with F̂ the empirical CDF of the training rows, then standardised

• AsinhScaler is the “Invariant” scaler of epftoolbox’s LEAR (Lago et al., 2021): median/MAD normalisation (the MAD divided by 0.6745 estimates the standard deviation of normal data), then the inverse hyperbolic sine. Near the median it is almost linear. For spikes it grows like a logarithm, and it is symmetric, so negative prices are fine. If the MAD is 0 (more than half of the training values are equal, e.g. a price floor) the sample standard deviation is used, and 1.0 if that is 0 too. The inverse is median + scale · sinh(z).
• NPITScaler is the normal probability integral transform. The i-th smallest of n training values gets F̂ = i / (n + 1) (tied values share their mid-rank), so every value maps to a finite normal quantile. Between training values the map is linear. Values outside the training range are clamped to the extreme knots: a transformed predictor can’t exceed the training range, and a forecast can’t go below the training window’s lowest or above its highest price.

Parameters

AsinhScaler and NPITScaler take one parameter:

Parameter	Type	Default	Description
apply_to	str or list	"all"	Which predictors get the VST besides the target: "all" (every non-binary predictor), "target" (none, predictors are standardised), or a list of glob patterns matched against the expanded predictor names, e.g. ["price", "price_d-*"]

StandardScaler takes no parameters.

Which columns are transformed

• The target always gets the VST.
• Predictors follow apply_to. The default "all" matches epftoolbox’s LEAR, which applies the Invariant scaler to every input except the day-of-week dummies. The VST papers transform the price series. apply_to=["price", "price_d-*"] does that and only standardises exogenous inputs such as load or weather. If no pattern matches any predictor, a warning says that only the target is transformed.
• Binary 0/1 predictors (dummies) are never changed, whatever apply_to says. The same rule as for StandardScaler decides what is binary.
• Every column gets its own parameters (median/MAD or empirical CDF), estimated from the task’s training rows.
• After the VST every transformed column, and the target, is standardised, so models always receive centred data with unit variance. This is why OLSModel, which fits without an intercept, stays valid. epftoolbox’s LEAR skips this step. An affine rescaling doesn’t change a least-squares fit with an intercept, but it does change the relative scale of the inputs that a Lasso penalty sees, so LassoCV results won’t match LEAR’s exactly.

No look-ahead

A fresh scaler is fitted for every (hour, horizon, run day) task on that task’s training rows only. The newest training target is the price of the day before the forecast is issued. The test row is transformed with the training parameters and never changes them. Don’t apply a VST to the whole data set in a DataPipeline: that would put information from the test period into the training data.

Back-transformed forecasts are median-type

The model is fitted to the transformed target, and its prediction is mapped back with the inverse VST. The inverse is monotone but non-linear, so it maps a median to a median but not a mean to a mean (E[sinh(Z)] ≠ sinh(E[Z])). A model fitted to the transformed target therefore gives, after back-transformation, roughly the conditional median price, not the mean. That suits MAE, which the median minimises. RMSE is minimised by the mean, and with skewed, spiky prices the back-transformed forecast can be biased for it. No bias correction is applied.

Caution

Result files are named after the model and resumed by (hour, horizon, day) only. Give each scaler variant its own name, otherwise a run with save_dir reuses forecasts made with the other scaler.

YAML

models:
- class: OLSModel
  params:
    predictors: [price_d-1, "load_forecast_d+{horizon}"]
    training_window: 365
    name: OLS asinh
    scaler: asinh
- class: LassoCVModel
  params:
    predictors: [price_d-1, "load_forecast_d+{horizon}"]
    name: Lasso N-PIT prices
    scaler:
      name: npit
      params:
        apply_to: [price, price_d-*]

A model without a scaler entry uses standard.

Not implemented

The shifted and mirror logarithm, Box-Cox, the parametrised asinh of Uniejewski (2026) and averaging forecasts across transformations are not available yet.

References

• B. Uniejewski, R. Weron, F. Ziel (2018). Variance stabilizing transformations for electricity spot price forecasting. IEEE Transactions on Power Systems 33(2). Compares 16 transformations on 12 markets. The normal PIT performed best.
• B. Uniejewski (2026). Variance stabilizing transformations for electricity price forecasting in periods of increased volatility. Electric Power Systems Research 257, 112992. arXiv:2511.13603. On German, Spanish and French data from 2015–2024, VSTs reduced LEAR errors by up to 14.6%.
• J. Lago, G. Marcjasz, B. De Schutter, R. Weron (2021). Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark. Applied Energy 293.