Forecasts time series using classical statistical models (ARIMA, SARIMAX, ETS, ARAR) wrapped in ForecasterStats. Covers model selection, Auto-ARIMA, backtesting statistical models, and parameter tuning. Use when the user wants traditional statistical forecasting methods.
See references/model-parameters.md for
complete constructor signatures of all statistical models (Arima, Sarimax,
Ets, Arar), the Ets model string format, Auto-ARIMA parameters, seasonal_order
differences between Arima and Sarimax, and grid search param_grid examples.
When to Use
Use statistical models when:
The series is short (< 200 observations)
Interpretability is important (ARIMA coefficients, ETS components)
You need built-in prediction intervals without residual bootstrapping
As a baseline to compare against ML models
Available Models
Model
相关技能
Class
Description
ARIMA
Arima
AutoRegressive Integrated Moving Average
Auto-ARIMA
Arima(order=None)
Automatic order selection
SARIMAX
Sarimax
ARIMA with exogenous variables (seasonal)
ETS
Ets
Exponential Smoothing (Error-Trend-Seasonal)
ARAR
Arar
Autoregressive model with memory shortening
Complete Workflow: ARIMA
import pandas as pd
from skforecast.recursive import ForecasterStats
from skforecast.stats import Arima
from skforecast.model_selection import backtesting_stats, TimeSeriesFold
# 1. Load data
data = pd.read_csv('data.csv', index_col='date', parse_dates=True)
data = data.asfreq('MS') # Monthly Start frequency
# 2. Manual ARIMA: specify order and seasonal_order
arima_model = Arima(
order=(1, 1, 1), # (p, d, q)
seasonal_order=(1, 1, 1), # (P, D, Q)
m=12, # Seasonal period
)
forecaster = ForecasterStats(estimator=arima_model)
forecaster.fit(y=data['target'])
predictions = forecaster.predict(steps=12)
# 3. Prediction intervals (all stat models support this natively,
# no bootstrapping needed). Accepts both `interval` and `alpha`.
predictions_interval = forecaster.predict_interval(
steps=12,
interval=[10, 90], # or use alpha=0.2 for 80% interval
)
Auto-ARIMA (Automatic Order Selection)
# Set order=None to enable automatic order selection
auto_arima = Arima(order=None, seasonal=True, m=12)
forecaster = ForecasterStats(estimator=auto_arima)
forecaster.fit(y=data['target'])
# Check selected order
print(forecaster.estimator.best_params_['order'])
print(forecaster.estimator.best_params_['seasonal_order'])
predictions = forecaster.predict(steps=12)
# Use model='ZZZ' (or model=None) to let ETS automatically select
# the best Error, Trend, and Seasonal components
auto_ets = Ets(model='ZZZ', m=12)
forecaster = ForecasterStats(estimator=auto_ets)
forecaster.fit(y=data['target'])
# Check the selected model configuration
print(forecaster.estimator.best_params_)
predictions = forecaster.predict(steps=12)
SARIMAX (with Exogenous Variables)
from skforecast.stats import Sarimax
sarimax_model = Sarimax(
order=(1, 1, 1),
seasonal_order=(1, 1, 1, 12), # (P, D, Q, seasonal_period)
)
forecaster = ForecasterStats(estimator=sarimax_model)
forecaster.fit(y=data['target'], exog=exog_train)
# For prediction, exog must cover the forecast horizon
predictions = forecaster.predict(steps=12, exog=exog_test)
cv = TimeSeriesFold(
steps=12,
initial_train_size=len(data) - 60,
refit=False,
)
metric, predictions_bt = backtesting_stats(
forecaster=forecaster,
y=data['target'],
cv=cv,
metric='mean_absolute_error',
freeze_params=True, # Params from first fit reused in refits (avoids re-running auto selection)
)
# If freeze_params=False, auto selection runs independently each fold and output
# includes an extra 'estimator_params' column with the parameters selected per fold.
Multiple Models Simultaneously
# ForecasterStats accepts a list of models — fits each independently
from skforecast.stats import Arima, Ets
models = [
Arima(order=(1, 1, 1), seasonal_order=(1, 1, 1), m=12),
Ets(model='AAA', m=12),
]
forecaster = ForecasterStats(estimator=models)
forecaster.fit(y=data['target'])
# predict returns DataFrame with one column per model
predictions = forecaster.predict(steps=12)
Common Mistakes
Using deprecated Ets(error=, trend=, seasonal=) syntax: Use Ets(model='AAA', m=12) with a model string instead.
Forgetting m parameter: ARIMA and ETS seasonal models require m (seasonal period).
Not using backtesting_stats: Use backtesting_stats() for statistical models, NOT backtesting_forecaster().
Using grid_search_forecaster for stats: Use grid_search_stats() or random_search_stats() instead.
Passing seasonal_order=(1,1,1,12) to Arima: Arima uses a 3-tuple seasonal_order=(P,D,Q) plus a separate m=12 parameter. The 4-tuple (P,D,Q,s) format is only for Sarimax.