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SARIMA

As explained in Time Series Forecasting Using Foundation Models

SARIMA is a seasonal autoregressive integrated moving-average model for forecasting time series with recurring seasonal structure.

SARIMA is a seasonal autoregressive integrated moving-average model for forecasting time series with recurring seasonal structure. It extends ARIMA with seasonal counterparts for autoregression, integration, and moving averages. section 10.2.3

Specify SARIMA with two parameter groups:

  • Use (p,d,q) for nonseasonal autoregressive order, integration order, and moving-average order. section 10.2.3
  • Use (P,D,Q) for the corresponding seasonal orders; with a seven-day season, seasonal lag 1 means lag 7. section 10.2.3
  • Try parameter combinations using a criterion such as AIC, which balances model complexity and overfitting. section 10.2.3

Daily blog-visit forecasting

For daily website visits with clear weekly seasonality, AutoARIMA selected SARIMA(2,0,1)(0,1,1): p=2, d=0, q=1, P=0, D=1, and Q=1. Cross-validation used 20 nonoverlapping seven-day windows and evaluated MAE and sMAPE. section 10.1 section 10.2.3

Listing 10.5 Fitting an AutoARIMA model
from statsforecast.arima import ARIMASummary  #1
from statsforecast.models import AutoARIMA

autoarima_model = AutoARIMA(season_length=7)
sf = StatsForecast(models=[autoarima_model], freq=FREQ)
init = time()
autoarima_cv_fcsts = sf.cross_validation(
    h=HORIZON,
    df=df,
    n_windows=N_WINDOWS,
    step_size=HORIZON
)
print(f"AutoARIMA time: {time() - init} seconds")
autoarima_cv_fcsts.to_csv("autoarima_preds.csv", header=True, index=False)

Use the AutoARIMA listing to configure a seven-day seasonal period and generate cross-validation forecasts with statsforecast. section 10.2.3

How Time Series Forecasting Using Foundation Models covers it

How deep it goes
Defines all six orders and demonstrates automated selection, but defers detailed SARIMA theory.
Examples
Uses daily website visits, weekly seasonal lag 7, AutoARIMA, and SARIMA(2,0,1)(0,1,1).
What it assumes
Assumes comfort with traditional forecasting techniques while briefly explaining ARIMA extensions and seasonal orders.
What you can do after
Apply it via AutoARIMA, inspect selected parameters, produce forecasts, and compare errors against a seasonal naïve baseline.
How it connects
Connects ARIMA with seasonality, AIC, AutoARIMA, cross-validation, MAE, and sMAPE.
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This explainer was generated by Manning's knowledge graph from the text of Time Series Forecasting Using Foundation Models. The section links point to the parts of the book it draws on.