Baseline Forecasting

Baseline Forecasting

When to Use

Use this skill to build a simple, explainable baseline with ForecasterEquivalentDate and to check whether a more complex model actually beats it. A baseline predicts each future step from an equivalent past date (e.g. same weekday last week), optionally aggregating several past occurrences.

Always establish a baseline before trusting an ML model: if the ML forecaster cannot beat the naive baseline, the added complexity is not justified.

Related skills

• Prerequisite: choosing-a-forecaster (decide whether a baseline or an ML model fits the problem)
• Alongside: forecasting-single-series (train the ML model you are benchmarking against)
• Next: metric-selection (use MASE to compare the model against the naive baseline)
• Next: hyperparameter-optimization (route: baselines are tuned with grid_search_equivalent_date, not the generic search)
• Next: prediction-intervals (add conformal intervals to the baseline)

Stop Conditions

Scan before writing code. Each row lists a rule, the symptom when it is broken, and the recovery.

Overview

ForecasterEquivalentDate has three modeling parameters:

• offset — how far back to look for the equivalent date. int (number of steps) or a pandas DateOffset (calendar-aware).
• n_offsets — how many equivalent dates to combine (default 1).
• agg_func — how to aggregate them when n_offsets > 1 (default np.mean).

import numpy as np
from skforecast.recursive import ForecasterEquivalentDate

# Predict each step as the value observed 7 steps earlier (seasonal-naive, weekly on daily data)
forecaster = ForecasterEquivalentDate(offset=7, n_offsets=1)
forecaster.fit(y=y_train)
predictions = forecaster.predict(steps=14)

offset: int vs pandas DateOffset

This is the part users get wrong most often.

• Integer offset — a fixed number of steps back. Works with a RangeIndex or a DatetimeIndex. offset=7 on daily data = "same day last week"; offset=24 on hourly data = "same hour yesterday".
• pandas DateOffset — a calendar rule (e.g. pd.offsets.Week, pd.offsets.BusinessDay). Requires a DatetimeIndex with a set frequency. Use it when the equivalent date must follow the calendar (business days, month ends, holidays) rather than a fixed step count.

import pandas as pd

# Integer offset: 7 steps back
forecaster = ForecasterEquivalentDate(offset=7)

# DateOffset: one calendar week back (needs a DatetimeIndex with frequency)
forecaster = ForecasterEquivalentDate(offset=pd.offsets.Week(1))

n_offsets and agg_func

Set n_offsets > 1 to combine several equivalent dates, aggregated by agg_func. offset and n_offsets are coupled (together they define the window), and agg_func decides how the values are pooled:

# Moving average of the last 7 observations: offset=1, n_offsets=7
forecaster = ForecasterEquivalentDate(offset=1, n_offsets=7, agg_func=np.mean)

# Mean of the values 7 and 14 steps back: offset=7, n_offsets=2
forecaster = ForecasterEquivalentDate(offset=7, n_offsets=2, agg_func=np.mean)

agg_func is a real, searchable parameter — do not forget it when comparing configurations (e.g. np.mean vs np.median).

Complete Workflow: backtest and compare against a model

from skforecast.model_selection import backtesting_forecaster, TimeSeriesFold
from skforecast.metrics import mean_absolute_scaled_error

cv = TimeSeriesFold(steps=7, initial_train_size=len(y) - 70, refit=False)

metric_baseline, _ = backtesting_forecaster(
    forecaster = ForecasterEquivalentDate(offset=7, n_offsets=1),
    y          = y,
    cv         = cv,
    metric     = mean_absolute_scaled_error,
)
# Backtest the ML model with the SAME `cv` and `metric`, then compare the two
# values: the lower error wins. For the model, MASE < 1 means it beats the
# in-sample naive forecast; MASE >= 1 means it does not.

See metric-selection for why MASE is the natural yardstick against a naive baseline.

Selecting a configuration

Use grid_search_equivalent_date (baselines are not compatible with the generic grid_search_forecaster). Because offset/n_offsets are coupled and agg_func is a third searchable parameter, prefer the list-of-configs form so every configuration is explicit:

from skforecast.model_selection import grid_search_equivalent_date, TimeSeriesFold

cv = TimeSeriesFold(steps=7, initial_train_size=len(y) - 70, refit=False)

results = grid_search_equivalent_date(
    forecaster = ForecasterEquivalentDate(offset=1, n_offsets=1),
    y          = y,
    cv         = cv,
    param_grid = [
        {'alias': '7-day moving average',     'offset': 1, 'n_offsets': 7, 'agg_func': np.mean},
        {'alias': 'mean of lag-7 and lag-14', 'offset': 7, 'n_offsets': 2, 'agg_func': np.mean},
        {'alias': 'median of lag-7 & lag-14', 'offset': 7, 'n_offsets': 2, 'agg_func': np.median},
    ],
    metric      = 'mean_absolute_error',
    return_best = True,
)

• dict form → Cartesian product (use only when every combination is meaningful).
• list form → one explicit configuration per dict (scalar values), avoiding meaningless offset/n_offsets combinations; each dict may carry an optional alias label that appears as the first results column.

Details and the full parameter table: hyperparameter-optimization (references/search-parameters.md).

Prediction intervals

ForecasterEquivalentDate supports conformal intervals only. Store residuals at fit time, then call predict_interval:

forecaster = ForecasterEquivalentDate(offset=7, n_offsets=1)
forecaster.fit(y=y_train, store_in_sample_residuals=True)
predictions = forecaster.predict_interval(steps=14, method='conformal', interval=[0.1, 0.9])

See prediction-intervals for the conformal method details.

Related API

Constructor and method signatures live in the complete-api-reference skill (references/forecaster-constructors.md and references/forecaster-methods.md). This skill covers the baseline workflow and its gotchas, not the full API surface.